1023:
52:
1435:. Adian later improved the bound on the odd exponent to 665. The latest improvement to the bound on odd exponent is 101 obtained by Adian himself in 2015. The case of even exponent turned out to be considerably more difficult. It was only in 1994 that Sergei Vasilievich Ivanov was able to prove an analogue of NovikovâAdian theorem: for any
1471:â„ 8000. NovikovâAdian, Ivanov and LysĂ«nok established considerably more precise results on the structure of the free Burnside groups. In the case of the odd exponent, all finite subgroups of the free Burnside groups were shown to be cyclic groups. In the even exponent case, each finite subgroup is contained in a product of two
928:
The case of even exponents turned out to be much harder to settle. In 1992, S. V. Ivanov announced the negative solution for sufficiently large even exponents divisible by a large power of 2 (detailed proofs were published in 1994 and occupied some 300 pages). Later joint work of Ol'shanskii and
911:
Nevertheless, the general answer to the
Burnside problem turned out to be negative. In 1964, Golod and Shafarevich constructed an infinite group of Burnside type without assuming that all elements have uniformly bounded order. In 1968,
1034:
Part of the difficulty with the general
Burnside problem is that the requirements of being finitely generated and periodic give very little information about the possible structure of a group. Therefore, we pose more requirements on
920:
supplied a negative solution to the bounded exponent problem for all odd exponents larger than 4381 which was later improved to an odd exponent larger than 665 by Adian and the best odd number bound is 101 also by Adian. In 1982,
1286:
is obtained from it by imposing additional relations. The existence of the free
Burnside group and its uniqueness up to an isomorphism are established by standard techniques of group theory. Thus if
1510:
in 1979 using geometric methods, thus affirmatively solving O. Yu. Schmidt's problem. In 1982 Ol'shanskii was able to strengthen his results to establish existence, for any sufficiently large
884:
was able to prove in 1958 that among the finite groups with a given number of generators and a given prime exponent, there exists a largest one. This provides a solution for the
848:
provided a counter-example in 1964. The problem has many refinements and variants that differ in the additional conditions imposed on the orders of the group elements (see
1498:
A famous class of counterexamples to the
Burnside problem is formed by finitely generated non-cyclic infinite groups in which every nontrivial proper subgroup is a finite
497:
472:
435:
925:
found some striking counterexamples for sufficiently large odd exponents (greater than 10), and supplied a considerably simpler proof based on geometric ideas.
1964:
933:, provided the exponent is sufficiently large. By contrast, when the exponent is small and different from 2, 3, 4 and 6, very little is known.
799:
1922:
proposed a nearly 300 page alternative proof to the
Burnside problem in 1973; however, Adian ultimately pointed out a flaw in that proof.
2307:
2287:
1787:
during the 1950s, prior to the negative solution of the general
Burnside problem. His solution, establishing the finiteness of B
357:
17:
1345:
The full solution to
Burnside problem in this form is not known. Burnside considered some easy cases in his original paper:
307:
2302:
1096:
It turns out that this problem can be restated as a question about the finiteness of groups in a particular family. The
792:
302:
2166:
2084:
1972:
1897:
1600:
has all finite limits and colimits. It can also be stated more explicitly in terms of certain universal groups with
1932:
Nahlus, Nazih; Yang, Yilong (2021). "Projective Limits and
Ultraproducts of Nonabelian Finite Groups". p. 19.
1592:
This variant of the
Burnside problem can also be stated in terms of category theory: an affirmative answer for all
1142:, and which is the "largest" group satisfying these requirements. More precisely, the characteristic property of B(
1529:. In a paper published in 1996, Ivanov and Ol'shanskii solved an analogue of the Burnside problem in an arbitrary
718:
1381:
1007:
785:
896:
had shown in 1911 that any finitely generated periodic group that was a subgroup of the group of invertible
2283:
1919:
1803:
in finite characteristic. The case of arbitrary exponent has been completely settled in the affirmative by
402:
216:
837:
134:
1369:
905:
817:
600:
334:
211:
99:
480:
455:
418:
2192:
Zel'manov, E I (1991). "Solution of the
Restricted Burnside Problem for Groups of Odd Exponent".
1476:
1223:
1521:> 10) of a finitely generated infinite group in which every nontrivial proper subgroup is a
750:
540:
1507:
922:
624:
965:= 1. Clearly, every finite group is periodic. There exist easily defined groups such as the
2257:
2201:
2126:
1503:
1420:
821:
564:
552:
170:
104:
1455:) is infinite; together with the NovikovâAdian theorem, this implies infiniteness for all
8:
1697:
1613:
139:
34:
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2217:
2142:
1933:
1299:
972:
which are infinite periodic groups; but the latter group cannot be finitely generated.
124:
96:
1419:
in 1968. Using a complicated combinatorial argument, they demonstrated that for every
2248:
Zel'manov, E I (1992). "A Solution of the Restricted Burnside Problem for 2-groups".
2162:
2146:
2080:
1968:
1893:
1585:
1480:
529:
372:
266:
2269:
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2213:
2138:
695:
2265:
2209:
2134:
2104:
2054:
2029:
2008:
1999:
Adian, S. I. (2015). "New estimates of odd exponents of infinite Burnside groups".
1988:
1609:
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930:
845:
829:
680:
672:
664:
656:
648:
636:
576:
516:
506:
348:
290:
165:
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2042:
1979:
S. I. Adian (2015). "New estimates of odd exponents of infinite Burnside groups".
929:
Ivanov established a negative solution to an analogue of the Burnside problem for
2020:
S. V. Ivanov (1994). "The Free Burnside Groups of Sufficiently Large Exponents".
1887:
1784:
1616:
in any group is itself a normal subgroup of finite index. Thus, the intersection
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341:
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314:
279:
200:
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175:
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114:
91:
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2012:
1992:
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was able to solve the restricted Burnside problem for an arbitrary exponent.)
2296:
2229:
2173:
2072:
1848:
1804:
1412:
1022:
913:
889:
868:
Initial work pointed towards the affirmative answer. For example, if a group
690:
612:
446:
319:
185:
27:
If G is a finitely generated group with exponent n, is G necessarily finite?
1956:
1808:
1522:
1511:
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1027:
992:
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150:
109:
80:
43:
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949:(or torsion) if every element has finite order; in other words, for each
893:
2178:"Solution of the restricted Burnside problem for groups of odd exponent"
2157:. Translated from the 1989 Russian original by Yu. A. Bakhturin (1991)
1596:
is equivalent to saying that the category of finite groups of exponent
1431:> 4381, there exist infinite, finitely generated groups of exponent
712:
440:
1892:. Dordrecht ; Boston: Kluwer Academic Publishers. p. xxii.
533:
2233:
2177:
2117:
Lysënok, I. G. (1996). "Infinite Burnside groups of even exponent".
1938:
70:
2161:(Soviet Series), 70. Dordrecht: Kluwer Academic Publishers Group.
2040:
2109:
2092:
1411:
The breakthrough in solving the Burnside problem was achieved by
1000:
412:
326:
1963:. Translated from the Russian by John Lennox and James Wiegold.
1636:). One can therefore define the free restricted Burnside group B
1847:, so that a free Burnside group of exponent two is necessarily
1043:
with the additional property that there exists a least integer
1030:
of the 27-element free Burnside group of rank 2 and exponent 3.
904:
complex matrices was finite; he used this theorem to prove the
51:
1873:
Representation Theory of Finite Groups and Associated Algebras
1073:. The Burnside problem for groups with bounded exponent asks:
1541:
Formulated in the 1930s, it asks another, related, question:
1475:, and there exist non-cyclic finite subgroups. Moreover, the
1380:
The following additional results are known (Burnside, Sanov,
1010:). However, the orders of the elements of this group are not
2043:"Hyperbolic groups and their quotients of bounded exponents"
1608:. By basic results of group theory, the intersection of two
2182:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
2097:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
1799:), used a relation with deep questions about identities in
2234:"Solution of the restricted Burnside problem for 2-groups"
1620:
of all the normal subgroups of the free Burnside group B(
1376:
copies of the cyclic group of order 2 and hence finite.
1318:. The Burnside problem can now be restated as follows:
872:
is finitely generated and the order of each element of
840:. It is known to have a negative answer in general, as
1740:). The restricted Burnside problem then asks whether B
991:
This question was answered in the negative in 1964 by
1981:
Trudy Matematicheskogo Instituta imeni V. A. Steklova
483:
458:
421:
2071:. Translated from the Russian and with a preface by
1870:
1752:) is a finite group. In terms of category theory, B
1628:) which have finite index is a normal subgroup of B(
1506:. First examples of such groups were constructed by
1483:
problems were shown to be effectively solvable in B(
2001:
Proceedings of the Steklov Institute of Mathematics
1463:℠2. This was improved in 1996 by I. G. Lysënok to
1728:) â in other words, it is a homomorphic image of B
832:in 1902, making it one of the oldest questions in
491:
466:
429:
2047:Transactions of the American Mathematical Society
983:is a finitely generated, periodic group, then is
888:for the case of prime exponent. (Later, in 1989,
2294:
2077:Ergebnisse der Mathematik und ihrer Grenzgebiete
2022:International Journal of Algebra and Computation
1965:Ergebnisse der Mathematik und ihrer Grenzgebiete
885:
853:
1827:The key step is to observe that the identities
1491:) both for the cases of odd and even exponents
1564:is bounded by some constant depending only on
1560:is finite, can one conclude that the order of
1536:
1059:= 1. A group with this property is said to be
2247:
2191:
2090:
1961:The Burnside problem and identities in groups
1772:in the category of finite groups of exponent
1572:? Equivalently, are there only finitely many
1408:The particular case of B(2, 5) remains open.
849:
793:
2019:
1290:is any finitely generated group of exponent
1084:is a finitely generated group with exponent
836:, and was influential in the development of
2228:
2172:
2093:"Infinite Burnside groups of even exponent"
1978:
1885:
1017:
936:
1931:
1925:
1875:. John Wiley & Sons. pp. 256â262.
1783:, this problem was extensively studied by
800:
786:
2108:
2058:
2041:S. V. Ivanov; A. Yu. Ol'Shanskii (1996).
1937:
1879:
856:below). Some of these variants are still
485:
460:
423:
2155:Geometry of defining relations in groups
1967:, 95. Springer-Verlag, Berlin-New York.
1889:Geometry of defining relations in groups
1871:Curtis, Charles; Reiner, Irving (1962).
1176:, there is a unique homomorphism from B(
1021:
2288:MacTutor History of Mathematics archive
2116:
1696:) with finite index. Therefore, by the
14:
2295:
358:Classification of finite simple groups
1998:
1864:
999:, who gave an example of an infinite
957:, there exists some positive integer
2079:(3) , 20. Springer-Verlag, Berlin.
24:
1779:In the case of the prime exponent
1533:for sufficiently large exponents.
820:in which every element has finite
25:
2319:
2277:
2194:Mathematics of the USSR-Izvestiya
1700:, every finite group of exponent
1664:. Every finite group of exponent
2308:Unsolved problems in mathematics
2159:Mathematics and its Applications
1006:that is finitely generated (see
863:
50:
2284:History of the Burnside problem
2270:10.1070/SM1992v072n02ABEH001272
2250:Mathematics of the USSR-Sbornik
2214:10.1070/IM1991v036n01ABEH001946
2139:10.1070/IM1996v060n03ABEH000077
1950:
1314:is the number of generators of
1913:
1821:
1672:generators is isomorphic to B(
1061:periodic with bounded exponent
1014:bounded by a single constant.
719:Infinite dimensional Lie group
13:
1:
2060:10.1090/S0002-9947-96-01510-3
1886:OlÊčshanskiÄ, A. Iïž UïžĄ (1991).
1858:
1708:generators is isomorphic to B
1333:is the free Burnside group B(
1548:If it is known that a group
1546:Restricted Burnside problem.
1447:divisible by 2, the group B(
1325:For which positive integers
1226:, the free Burnside group B(
1039:. Consider a periodic group
492:{\displaystyle \mathbb {Z} }
467:{\displaystyle \mathbb {Z} }
430:{\displaystyle \mathbb {Z} }
7:
1537:Restricted Burnside problem
1150:) is that, given any group
1138:= 1 holds for all elements
886:restricted Burnside problem
217:List of group theory topics
10:
2324:
2303:Combinatorial group theory
2153:A. Yu. Ol'shanskii (1989)
1839:) = 1 together imply that
1688:is a normal subgroup of B(
838:combinatorial group theory
2034:10.1142/S0218196794000026
2013:10.1134/S0081543815040045
1993:10.1134/S0371968515020041
1698:Third Isomorphism Theorem
1120:distinguished generators
1008:GolodâShafarevich theorem
977:General Burnside problem.
1814:
1604:generators and exponent
1556:generators and exponent
1400:, 6) are finite for all
1018:Bounded Burnside problem
937:General Burnside problem
876:is a divisor of 4, then
818:finitely generated group
335:Elementary abelian group
212:Glossary of group theory
2238:Matematicheskii Sbornik
2067:A. I. Kostrikin (1990)
1768:cyclic groups of order
1764:) is the coproduct of
1580:generators of exponent
1282:generators of exponent
18:Burnside's problem
2119:Izvestiya: Mathematics
2091:I. G. Lysënok (1996).
1811:in 1994 for his work.
1807:, who was awarded the
1590:
1343:
1134:in which the identity
1094:
1031:
989:
824:must necessarily be a
751:Linear algebraic group
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468:
431:
1543:
1320:
1222:. In the language of
1075:
1025:
974:
880:is finite. Moreover,
494:
469:
432:
1323:Burnside problem II.
906:JordanâSchur theorem
481:
456:
419:
2262:1992SbMat..72..543Z
2206:1991IzMat..36...41Z
2131:1996IzMat..60..453L
1439:> 1 and an even
1224:group presentations
1116:), is a group with
1098:free Burnside group
1092:necessarily finite?
1078:Burnside problem I.
1068:group with exponent
987:necessarily finite?
125:Group homomorphisms
35:Algebraic structure
1508:A. Yu. Ol'shanskii
1256:= 1 for each word
1252:and the relations
1047:such that for all
1032:
923:A. Yu. Ol'shanskii
828:. It was posed by
601:Special orthogonal
489:
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308:Lagrange's theorem
1300:homomorphic image
931:hyperbolic groups
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1531:hyperbolic group
1502:, the so-called
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1172:and of exponent
997:Igor Shafarevich
846:Igor Shafarevich
830:William Burnside
814:Burnside problem
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1997:Translation in
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2278:External links
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2256:(2): 543â565.
2240:(in Russian).
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2184:(in Russian).
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2125:(3): 453â654.
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1607:
1603:
1599:
1595:
1589:
1587:
1583:
1579:
1575:
1571:
1567:
1563:
1559:
1555:
1551:
1547:
1542:
1534:
1532:
1528:
1524:
1520:
1516:
1513:
1509:
1505:
1501:
1496:
1494:
1490:
1486:
1482:
1478:
1474:
1470:
1466:
1462:
1458:
1454:
1450:
1446:
1442:
1438:
1434:
1430:
1426:
1422:
1418:
1414:
1413:Pyotr Novikov
1409:
1403:
1399:
1395:
1391:
1387:
1386:
1385:
1383:
1375:
1371:
1367:
1363:
1360:
1356:
1352:
1348:
1347:
1346:
1342:
1340:
1336:
1332:
1328:
1324:
1319:
1317:
1313:
1309:
1305:
1301:
1297:
1293:
1289:
1285:
1281:
1277:
1273:
1263:
1259:
1255:
1251:
1241:
1237:
1233:
1229:
1225:
1221:
1217:
1211:th generator
1210:
1206:
1202:
1198:
1192:th generator
1191:
1187:
1183:
1179:
1175:
1171:
1161:
1157:
1153:
1149:
1145:
1141:
1137:
1133:
1123:
1119:
1115:
1111:
1107:
1104:and exponent
1103:
1099:
1093:
1091:
1087:
1083:
1079:
1074:
1072:
1069:
1065:
1062:
1058:
1054:
1050:
1046:
1042:
1038:
1029:
1024:
1015:
1013:
1009:
1005:
1003:
998:
994:
988:
986:
982:
978:
973:
971:
969:
964:
960:
956:
952:
948:
944:
934:
932:
926:
924:
919:
915:
914:Pyotr Novikov
909:
907:
903:
899:
895:
891:
890:Efim Zelmanov
887:
883:
879:
875:
871:
864:Brief history
861:
859:
855:
851:
847:
843:
839:
835:
831:
827:
823:
819:
815:
803:
798:
796:
791:
789:
784:
783:
781:
780:
773:
770:
769:
766:
763:
762:
759:
756:
755:
752:
749:
748:
745:
740:
739:
729:
726:
723:
722:
720:
714:
711:
709:
706:
705:
702:
699:
697:
694:
692:
689:
688:
685:
679:
677:
671:
669:
663:
661:
655:
653:
647:
646:
642:
638:
635:
634:
630:
626:
623:
622:
618:
614:
611:
610:
606:
602:
599:
598:
594:
590:
587:
586:
582:
578:
575:
574:
570:
566:
563:
562:
558:
554:
551:
550:
547:
544:
542:
539:
538:
535:
531:
526:
525:
518:
515:
513:
510:
508:
505:
504:
476:
451:
450:
448:
442:
439:
414:
411:
410:
404:
401:
399:
396:
395:
391:
390:
379:
376:
374:
371:
368:
365:
364:
363:
362:
359:
356:
355:
350:
347:
346:
343:
340:
339:
336:
333:
331:
329:
325:
324:
321:
318:
316:
313:
312:
309:
306:
304:
301:
300:
299:
298:
292:
289:
286:
281:
278:
277:
273:
268:
265:
262:
257:
254:
251:
246:
243:
242:
241:
240:
235:
234:Finite groups
230:
229:
218:
215:
213:
210:
209:
208:
207:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
177:
174:
172:
169:
167:
164:
162:
159:
157:
154:
152:
149:
148:
147:
146:
141:
138:
136:
133:
132:
131:
130:
127:
126:
122:
121:
116:
113:
111:
108:
106:
103:
101:
98:
95:
93:
90:
89:
88:
87:
82:
79:
77:
74:
72:
69:
68:
67:
66:
61:Basic notions
58:
57:
53:
49:
48:
45:
40:
36:
32:
31:
19:
2253:
2249:
2241:
2237:
2200:(1): 41â60.
2197:
2193:
2185:
2181:
2158:
2154:
2122:
2118:
2110:10.4213/im77
2103:(3): 3â224.
2100:
2096:
2076:
2068:
2050:
2046:
2025:
2021:
2007:(1): 33â71.
2004:
2000:
1984:
1980:
1960:
1951:Bibliography
1927:
1920:John Britton
1915:
1903:. Retrieved
1888:
1881:
1872:
1866:
1844:
1840:
1836:
1832:
1828:
1823:
1809:Fields Medal
1801:Lie algebras
1796:
1792:
1780:
1778:
1773:
1769:
1765:
1761:
1757:
1749:
1745:
1737:
1733:
1725:
1721:
1717:
1713:
1705:
1701:
1693:
1689:
1685:
1681:
1677:
1673:
1669:
1665:
1661:
1657:
1653:
1648:) to be the
1645:
1641:
1633:
1629:
1625:
1621:
1617:
1605:
1601:
1597:
1593:
1591:
1581:
1577:
1576:groups with
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1545:
1544:
1540:
1526:
1523:cyclic group
1518:
1514:
1512:prime number
1500:cyclic group
1497:
1492:
1488:
1484:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1432:
1428:
1424:
1417:Sergei Adian
1410:
1407:
1401:
1397:
1396:, 4), and B(
1393:
1389:
1379:
1373:
1368:, 2) is the
1365:
1358:
1355:cyclic group
1350:
1344:
1338:
1334:
1330:
1326:
1322:
1321:
1315:
1311:
1307:
1303:
1295:
1291:
1287:
1283:
1279:
1275:
1268:
1261:
1257:
1253:
1246:
1239:
1235:
1231:
1227:
1219:
1212:
1208:
1204:
1200:
1193:
1189:
1185:
1181:
1177:
1173:
1166:
1159:
1155:
1151:
1147:
1143:
1139:
1135:
1128:
1121:
1117:
1113:
1109:
1108:, denoted B(
1105:
1101:
1097:
1095:
1089:
1085:
1081:
1077:
1076:
1070:
1067:
1066:, or just a
1063:
1060:
1056:
1052:
1048:
1044:
1040:
1036:
1033:
1028:Cayley graph
1011:
1001:
993:Evgeny Golod
990:
984:
980:
976:
975:
967:
962:
958:
954:
950:
942:
940:
927:
918:Sergei Adian
910:
901:
897:
877:
873:
869:
867:
842:Evgeny Golod
834:group theory
826:finite group
813:
811:
640:
628:
616:
604:
592:
580:
568:
556:
327:
284:
271:
260:
249:
245:Cyclic group
123:
110:Free product
81:Group action
44:Group theory
39:Group theory
38:
2230:E. Zelmanov
2174:E. Zelmanov
1957:S. I. Adian
1586:isomorphism
1467:> 1 and
1459:> 1 and
1238:generators
1207:) into the
1158:generators
894:Issai Schur
530:Topological
369:alternating
2297:Categories
1939:2107.09900
1859:References
1612:of finite
961:such that
945:is called
854:restricted
637:Symplectic
577:Orthogonal
534:Lie groups
441:Free group
166:continuous
105:Direct sum
2147:250838960
2028:: 1â308.
1987:: 41â82.
1525:of order
1481:conjugacy
1357:of order
1353:) is the
1341:) finite?
1310:), where
701:Conformal
589:Euclidean
196:nilpotent
2232:(1991).
2222:39623037
2176:(1990).
1905:26 April
1584:, up to
1392:, 3), B(
1100:of rank
1012:a priori
947:periodic
941:A group
696:Poincaré
541:Solenoid
413:Integers
403:Lattices
378:sporadic
373:Lie type
201:solvable
191:dihedral
176:additive
161:infinite
71:Subgroup
2258:Bibcode
2202:Bibcode
2127:Bibcode
1959:(1979)
1849:abelian
1423:number
1382:M. Hall
1294:, then
1267:, ...,
1245:, ...,
1165:, ...,
1127:, ...,
850:bounded
691:Lorentz
613:Unitary
512:Lattice
452:PSL(2,
186:abelian
97:(Semi-)
2220:
2165:
2145:
2083:
1971:
1896:
1684:where
1574:finite
1234:) has
1004:-group
970:-group
546:Circle
477:SL(2,
366:cyclic
330:-group
181:cyclic
156:finite
151:simple
135:kernel
2218:S2CID
2143:S2CID
1934:arXiv
1815:Notes
1704:with
1668:with
1614:index
1552:with
1443:â„ 2,
1427:with
1349:B(1,
1302:of B(
1298:is a
1278:with
1199:of B(
1184:) to
1154:with
1088:, is
822:order
730:Sp(â)
727:SU(â)
140:image
2163:ISBN
2081:ISBN
1969:ISBN
1907:2024
1894:ISBN
1568:and
1479:and
1477:word
1415:and
1218:of
1026:The
995:and
916:and
852:and
844:and
812:The
724:O(â)
713:Loop
532:and
2286:at
2266:doi
2242:182
2210:doi
2135:doi
2105:doi
2055:doi
2051:348
2030:doi
2009:doi
2005:289
1989:doi
1985:289
1835:= (
1776:.
1720:)/(
1421:odd
1384:):
1372:of
1260:in
1080:If
1051:in
979:If
953:in
639:Sp(
627:SU(
603:SO(
567:SL(
555:GL(
2299::
2264:.
2254:72
2252:.
2236:.
2216:.
2208:.
2198:36
2196:.
2186:54
2180:.
2141:.
2133:.
2123:60
2121:.
2101:60
2095:.
2075:.
2049:.
2045:.
2026:04
2024:.
2003:.
1845:ba
1843:=
1841:ab
1837:ab
1831:=
1795:,
1760:,
1748:,
1736:,
1680:)/
1660:)/
1656:,
1652:B(
1644:,
1632:,
1624:,
1495:.
1487:,
1451:,
1388:B(
1364:B(
1337:,
1329:,
1306:,
1230:,
1203:,
1180:,
1146:,
1112:,
1055:,
908:.
900:Ă
860:.
615:U(
591:E(
579:O(
37:â
2272:.
2268::
2260::
2224:.
2212::
2204::
2169:.
2149:.
2137::
2129::
2113:.
2107::
2087:.
2063:.
2057::
2036:.
2032::
2015:.
2011::
1995:.
1991::
1975:.
1942:.
1936::
1909:.
1851:.
1833:b
1829:a
1797:p
1793:m
1791:(
1789:0
1781:p
1774:n
1770:m
1766:n
1762:n
1758:m
1756:(
1754:0
1750:n
1746:m
1744:(
1742:0
1738:n
1734:m
1732:(
1730:0
1726:M
1724:/
1722:N
1718:n
1716:,
1714:m
1712:(
1710:0
1706:m
1702:n
1694:n
1692:,
1690:m
1686:N
1682:N
1678:n
1676:,
1674:m
1670:m
1666:n
1662:M
1658:n
1654:m
1646:n
1642:m
1640:(
1638:0
1634:n
1630:m
1626:n
1622:m
1618:M
1606:n
1602:m
1598:n
1594:m
1588:?
1582:n
1578:m
1570:n
1566:m
1562:G
1558:n
1554:m
1550:G
1527:p
1519:p
1515:p
1493:n
1489:n
1485:m
1469:n
1465:m
1461:n
1457:m
1453:n
1449:m
1445:n
1441:n
1437:m
1433:n
1429:n
1425:n
1404:.
1402:m
1398:m
1394:m
1390:m
1374:m
1366:m
1361:.
1359:n
1351:n
1339:n
1335:m
1331:n
1327:m
1316:G
1312:m
1308:n
1304:m
1296:G
1292:n
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1284:n
1280:m
1276:G
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1269:x
1265:1
1262:x
1258:x
1254:x
1249:m
1247:x
1243:1
1240:x
1236:m
1232:n
1228:m
1220:G
1215:i
1213:g
1209:i
1205:n
1201:m
1196:i
1194:x
1190:i
1186:G
1182:n
1178:m
1174:n
1169:m
1167:g
1163:1
1160:g
1156:m
1152:G
1148:n
1144:m
1140:x
1136:x
1131:m
1129:x
1125:1
1122:x
1118:m
1114:n
1110:m
1106:n
1102:m
1090:G
1086:n
1082:G
1071:n
1064:n
1057:g
1053:G
1049:g
1045:n
1041:G
1037:G
1002:p
985:G
981:G
968:p
963:g
959:n
955:G
951:g
943:G
902:n
898:n
878:G
874:G
870:G
801:e
794:t
787:v
683:8
681:E
675:7
673:E
667:6
665:E
659:4
657:F
651:2
649:G
643:)
641:n
631:)
629:n
619:)
617:n
607:)
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595:)
593:n
583:)
581:n
571:)
569:n
559:)
557:n
499:)
486:Z
474:)
461:Z
437:)
424:Z
415:(
328:p
293:Q
285:n
282:D
272:n
269:A
261:n
258:S
250:n
247:Z
20:)
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