1012:
41:
1424:. 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
1460: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
917:
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
900:
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,
1023:
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
909:
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,
1275:
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
1499:
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
873:
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
837:
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
1487:
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
486:
461:
424:
914:
found some striking counterexamples for sufficiently large odd exponents (greater than 10), and supplied a considerably simpler proof based on geometric ideas.
1953:
922:, 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.
788:
1911:
proposed a nearly 300 page alternative proof to the
Burnside problem in 1973; however, Adian ultimately pointed out a flaw in that proof.
2296:
2276:
1776:
during the 1950s, prior to the negative solution of the general
Burnside problem. His solution, establishing the finiteness of B
346:
1334:
The full solution to
Burnside problem in this form is not known. Burnside considered some easy cases in his original paper:
296:
2291:
1085:
It turns out that this problem can be restated as a question about the finiteness of groups in a particular family. The
781:
291:
2155:
2073:
1961:
1886:
1589:
has all finite limits and colimits. It can also be stated more explicitly in terms of certain universal groups with
1921:
Nahlus, Nazih; Yang, Yilong (2021). "Projective Limits and
Ultraproducts of Nonabelian Finite Groups". p. 19.
1581:
This variant of the
Burnside problem can also be stated in terms of category theory: an affirmative answer for all
1131:, and which is the "largest" group satisfying these requirements. More precisely, the characteristic property of B(
1518:. In a paper published in 1996, Ivanov and Ol'shanskii solved an analogue of the Burnside problem in an arbitrary
707:
1370:
996:
774:
885:
had shown in 1911 that any finitely generated periodic group that was a subgroup of the group of invertible
2272:
1908:
1792:
in finite characteristic. The case of arbitrary exponent has been completely settled in the affirmative by
391:
205:
826:
123:
1358:
894:
806:
589:
323:
200:
88:
469:
444:
407:
2181:
Zel'manov, E I (1991). "Solution of the
Restricted Burnside Problem for Groups of Odd Exponent".
1465:
1212:
1510:> 10) of a finitely generated infinite group in which every nontrivial proper subgroup is a
739:
529:
1496:
911:
613:
954:= 1. Clearly, every finite group is periodic. There exist easily defined groups such as the
2246:
2190:
2115:
1492:
1409:
810:
553:
541:
159:
93:
1444:) is infinite; together with the NovikovâAdian theorem, this implies infiniteness for all
8:
1686:
1602:
128:
23:
2250:
2194:
2119:
2206:
2131:
1922:
1288:
961:
which are infinite periodic groups; but the latter group cannot be finitely generated.
113:
85:
1408:
in 1968. Using a complicated combinatorial argument, they demonstrated that for every
2237:
Zel'manov, E I (1992). "A Solution of the Restricted Burnside Problem for 2-groups".
2151:
2135:
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1957:
1882:
1574:
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518:
361:
255:
2258:
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2202:
2127:
684:
2254:
2198:
2123:
2093:
2043:
2018:
1997:
1988:
Adian, S. I. (2015). "New estimates of odd exponents of infinite Burnside groups".
1977:
1598:
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985:
919:
834:
818:
669:
661:
653:
645:
637:
625:
565:
505:
495:
337:
279:
154:
2048:
2031:
1968:
S. I. Adian (2015). "New estimates of odd exponents of infinite Burnside groups".
918:
Ivanov established a negative solution to an analogue of the Burnside problem for
2009:
S. V. Ivanov (1994). "The Free Burnside Groups of Sufficiently Large Exponents".
1876:
1773:
1605:
in any group is itself a normal subgroup of finite index. Thus, the intersection
870:
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732:
689:
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500:
330:
244:
184:
64:
955:
1638:
1461:
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386:
366:
303:
268:
189:
179:
164:
149:
103:
80:
2022:
2001:
1981:
881:
was able to solve the restricted Burnside problem for an arbitrary exponent.)
2285:
2218:
2162:
2061:
1837:
1793:
1401:
1011:
902:
878:
857:
Initial work pointed towards the affirmative answer. For example, if a group
679:
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435:
308:
174:
16:
If G is a finitely generated group with exponent n, is G necessarily finite?
1945:
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1511:
1500:
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233:
222:
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144:
139:
98:
69:
32:
1789:
938:(or torsion) if every element has finite order; in other words, for each
882:
2167:"Solution of the restricted Burnside problem for groups of odd exponent"
2146:. Translated from the 1989 Russian original by Yu. A. Bakhturin (1991)
1585:
is equivalent to saying that the category of finite groups of exponent
1420:> 4381, there exist infinite, finitely generated groups of exponent
701:
429:
1881:. Dordrecht ; Boston: Kluwer Academic Publishers. p. xxii.
522:
2222:
2166:
2106:
Lysënok, I. G. (1996). "Infinite Burnside groups of even exponent".
1927:
59:
2150:(Soviet Series), 70. Dordrecht: Kluwer Academic Publishers Group.
2029:
2098:
2081:
1400:
The breakthrough in solving the Burnside problem was achieved by
989:
401:
315:
1952:. Translated from the Russian by John Lennox and James Wiegold.
1625:). One can therefore define the free restricted Burnside group B
1836:, so that a free Burnside group of exponent two is necessarily
1032:
with the additional property that there exists a least integer
1019:
of the 27-element free Burnside group of rank 2 and exponent 3.
893:
complex matrices was finite; he used this theorem to prove the
40:
1862:
Representation Theory of Finite Groups and Associated Algebras
1062:. The Burnside problem for groups with bounded exponent asks:
1530:
Formulated in the 1930s, it asks another, related, question:
1464:, and there exist non-cyclic finite subgroups. Moreover, the
1369:
The following additional results are known (Burnside, Sanov,
999:). However, the orders of the elements of this group are not
2032:"Hyperbolic groups and their quotients of bounded exponents"
1597:. By basic results of group theory, the intersection of two
2171:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
2086:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya
1788:), used a relation with deep questions about identities in
2223:"Solution of the restricted Burnside problem for 2-groups"
1609:
of all the normal subgroups of the free Burnside group B(
1365:
copies of the cyclic group of order 2 and hence finite.
1307:. The Burnside problem can now be restated as follows:
861:
is finitely generated and the order of each element of
829:. It is known to have a negative answer in general, as
1729:). The restricted Burnside problem then asks whether B
980:
This question was answered in the negative in 1964 by
1970:
Trudy Matematicheskogo Instituta imeni V. A. Steklova
472:
447:
410:
2060:. Translated from the Russian and with a preface by
1859:
1741:) is a finite group. In terms of category theory, B
1617:) which have finite index is a normal subgroup of B(
1495:. First examples of such groups were constructed by
1472:
problems were shown to be effectively solvable in B(
1990:
Proceedings of the Steklov Institute of Mathematics
1452:℠2. This was improved in 1996 by I. G. Lysënok to
1717:) â in other words, it is a homomorphic image of B
821:in 1902, making it one of the oldest questions in
480:
455:
418:
2036:Transactions of the American Mathematical Society
972:is a finitely generated, periodic group, then is
877:for the case of prime exponent. (Later, in 1989,
2283:
2066:Ergebnisse der Mathematik und ihrer Grenzgebiete
2011:International Journal of Algebra and Computation
1954:Ergebnisse der Mathematik und ihrer Grenzgebiete
874:
842:
1816:The key step is to observe that the identities
1480:) both for the cases of odd and even exponents
1553:is bounded by some constant depending only on
1549:is finite, can one conclude that the order of
1525:
1048:= 1. A group with this property is said to be
2236:
2180:
2079:
1950:The Burnside problem and identities in groups
1761:in the category of finite groups of exponent
1561:? Equivalently, are there only finitely many
1397:The particular case of B(2, 5) remains open.
838:
782:
2008:
1279:is any finitely generated group of exponent
1073:is a finitely generated group with exponent
825:, and was influential in the development of
2217:
2161:
2082:"Infinite Burnside groups of even exponent"
1967:
1874:
1006:
925:
1920:
1914:
1864:. John Wiley & Sons. pp. 256â262.
1772:, this problem was extensively studied by
789:
775:
2097:
2047:
2030:S. V. Ivanov; A. Yu. Ol'Shanskii (1996).
1926:
1868:
845:below). Some of these variants are still
474:
449:
412:
2144:Geometry of defining relations in groups
1956:, 95. Springer-Verlag, Berlin-New York.
1878:Geometry of defining relations in groups
1860:Curtis, Charles; Reiner, Irving (1962).
1165:, there is a unique homomorphism from B(
1010:
2277:MacTutor History of Mathematics archive
2105:
1685:) with finite index. Therefore, by the
2284:
347:Classification of finite simple groups
1987:
1853:
988:, who gave an example of an infinite
946:, there exists some positive integer
2068:(3) , 20. Springer-Verlag, Berlin.
13:
1768:In the case of the prime exponent
1522:for sufficiently large exponents.
809:in which every element has finite
14:
2308:
2266:
2183:Mathematics of the USSR-Izvestiya
1689:, every finite group of exponent
1653:. Every finite group of exponent
2297:Unsolved problems in mathematics
2148:Mathematics and its Applications
995:that is finitely generated (see
852:
39:
2273:History of the Burnside problem
2259:10.1070/SM1992v072n02ABEH001272
2239:Mathematics of the USSR-Sbornik
2203:10.1070/IM1991v036n01ABEH001946
2128:10.1070/IM1996v060n03ABEH000077
1939:
1303:is the number of generators of
1902:
1810:
1661:generators is isomorphic to B(
1050:periodic with bounded exponent
1003:bounded by a single constant.
708:Infinite dimensional Lie group
1:
2049:10.1090/S0002-9947-96-01510-3
1875:OlÊčshanskiÄ, A. Iïž UïžĄ (1991).
1847:
1697:generators is isomorphic to B
1322:is the free Burnside group B(
1537:If it is known that a group
1535:Restricted Burnside problem.
1436:divisible by 2, the group B(
1314:For which positive integers
1215:, the free Burnside group B(
1028:. Consider a periodic group
481:{\displaystyle \mathbb {Z} }
456:{\displaystyle \mathbb {Z} }
419:{\displaystyle \mathbb {Z} }
7:
1526:Restricted Burnside problem
1139:) is that, given any group
1127:= 1 holds for all elements
875:restricted Burnside problem
206:List of group theory topics
10:
2313:
2292:Combinatorial group theory
2142:A. Yu. Ol'shanskii (1989)
1828:) = 1 together imply that
1677:is a normal subgroup of B(
827:combinatorial group theory
2023:10.1142/S0218196794000026
2002:10.1134/S0081543815040045
1982:10.1134/S0371968515020041
1687:Third Isomorphism Theorem
1109:distinguished generators
997:GolodâShafarevich theorem
966:General Burnside problem.
1803:
1593:generators and exponent
1545:generators and exponent
1389:, 6) are finite for all
1007:Bounded Burnside problem
926:General Burnside problem
865:is a divisor of 4, then
807:finitely generated group
324:Elementary abelian group
201:Glossary of group theory
2227:Matematicheskii Sbornik
2056:A. I. Kostrikin (1990)
1757:cyclic groups of order
1753:) is the coproduct of
1569:generators of exponent
1271:generators of exponent
2108:Izvestiya: Mathematics
2080:I. G. Lysënok (1996).
1800:in 1994 for his work.
1796:, who was awarded the
1579:
1332:
1123:in which the identity
1083:
1020:
978:
813:must necessarily be a
740:Linear algebraic group
482:
457:
420:
1532:
1309:
1211:. In the language of
1064:
1014:
963:
869:is finite. Moreover,
483:
458:
421:
1312:Burnside problem II.
895:JordanâSchur theorem
470:
445:
408:
2251:1992SbMat..72..543Z
2195:1991IzMat..36...41Z
2120:1996IzMat..60..453L
1428:> 1 and an even
1213:group presentations
1105:), is a group with
1087:free Burnside group
1081:necessarily finite?
1067:Burnside problem I.
1057:group with exponent
976:necessarily finite?
114:Group homomorphisms
24:Algebraic structure
1497:A. Yu. Ol'shanskii
1245:= 1 for each word
1241:and the relations
1036:such that for all
1021:
912:A. Yu. Ol'shanskii
817:. It was posed by
590:Special orthogonal
478:
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297:Lagrange's theorem
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1520:hyperbolic group
1491:, the so-called
1263:, and any group
1161:and of exponent
986:Igor Shafarevich
835:Igor Shafarevich
819:William Burnside
803:Burnside problem
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1986:Translation in
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2267:External links
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2245:(2): 543â565.
2229:(in Russian).
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2173:(in Russian).
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1560:
1556:
1552:
1548:
1544:
1540:
1536:
1531:
1523:
1521:
1517:
1513:
1509:
1505:
1502:
1498:
1494:
1490:
1485:
1483:
1479:
1475:
1471:
1467:
1463:
1459:
1455:
1451:
1447:
1443:
1439:
1435:
1431:
1427:
1423:
1419:
1415:
1411:
1407:
1403:
1402:Pyotr Novikov
1398:
1392:
1388:
1384:
1380:
1376:
1375:
1374:
1372:
1364:
1360:
1356:
1352:
1349:
1345:
1341:
1337:
1336:
1335:
1331:
1329:
1325:
1321:
1317:
1313:
1308:
1306:
1302:
1298:
1294:
1290:
1286:
1282:
1278:
1274:
1270:
1266:
1262:
1252:
1248:
1244:
1240:
1230:
1226:
1222:
1218:
1214:
1210:
1206:
1200:th generator
1199:
1195:
1191:
1187:
1181:th generator
1180:
1176:
1172:
1168:
1164:
1160:
1150:
1146:
1142:
1138:
1134:
1130:
1126:
1122:
1112:
1108:
1104:
1100:
1096:
1093:and exponent
1092:
1088:
1082:
1080:
1076:
1072:
1068:
1063:
1061:
1058:
1054:
1051:
1047:
1043:
1039:
1035:
1031:
1027:
1018:
1013:
1004:
1002:
998:
994:
992:
987:
983:
977:
975:
971:
967:
962:
960:
958:
953:
949:
945:
941:
937:
933:
923:
921:
915:
913:
908:
904:
903:Pyotr Novikov
898:
896:
892:
888:
884:
880:
879:Efim Zelmanov
876:
872:
868:
864:
860:
853:Brief history
850:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
808:
804:
792:
787:
785:
780:
778:
773:
772:
770:
769:
762:
759:
758:
755:
752:
751:
748:
745:
744:
741:
738:
737:
734:
729:
728:
718:
715:
712:
711:
709:
703:
700:
698:
695:
694:
691:
688:
686:
683:
681:
678:
677:
674:
668:
666:
660:
658:
652:
650:
644:
642:
636:
635:
631:
627:
624:
623:
619:
615:
612:
611:
607:
603:
600:
599:
595:
591:
588:
587:
583:
579:
576:
575:
571:
567:
564:
563:
559:
555:
552:
551:
547:
543:
540:
539:
536:
533:
531:
528:
527:
524:
520:
515:
514:
507:
504:
502:
499:
497:
494:
493:
465:
440:
439:
437:
431:
428:
403:
400:
399:
393:
390:
388:
385:
384:
380:
379:
368:
365:
363:
360:
357:
354:
353:
352:
351:
348:
345:
344:
339:
336:
335:
332:
329:
328:
325:
322:
320:
318:
314:
313:
310:
307:
305:
302:
301:
298:
295:
293:
290:
289:
288:
287:
281:
278:
275:
270:
267:
266:
262:
257:
254:
251:
246:
243:
240:
235:
232:
231:
230:
229:
224:
223:Finite groups
219:
218:
207:
204:
202:
199:
198:
197:
196:
191:
188:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
146:
143:
141:
138:
137:
136:
135:
130:
127:
125:
122:
121:
120:
119:
116:
115:
111:
110:
105:
102:
100:
97:
95:
92:
90:
87:
84:
82:
79:
78:
77:
76:
71:
68:
66:
63:
61:
58:
57:
56:
55:
50:Basic notions
47:
46:
42:
38:
37:
34:
29:
25:
21:
20:
2242:
2238:
2230:
2226:
2189:(1): 41â60.
2186:
2182:
2174:
2170:
2147:
2143:
2111:
2107:
2099:10.4213/im77
2092:(3): 3â224.
2089:
2085:
2065:
2057:
2039:
2035:
2014:
2010:
1996:(1): 33â71.
1993:
1989:
1973:
1969:
1949:
1940:Bibliography
1916:
1909:John Britton
1904:
1892:. Retrieved
1877:
1870:
1861:
1855:
1833:
1829:
1825:
1821:
1817:
1812:
1798:Fields Medal
1790:Lie algebras
1785:
1781:
1769:
1767:
1762:
1758:
1754:
1750:
1746:
1738:
1734:
1726:
1722:
1714:
1710:
1706:
1702:
1694:
1690:
1682:
1678:
1674:
1670:
1666:
1662:
1658:
1654:
1650:
1646:
1642:
1637:) to be the
1634:
1630:
1622:
1618:
1614:
1610:
1606:
1594:
1590:
1586:
1582:
1580:
1570:
1566:
1565:groups with
1562:
1558:
1554:
1550:
1546:
1542:
1538:
1534:
1533:
1529:
1515:
1512:cyclic group
1507:
1503:
1501:prime number
1489:cyclic group
1486:
1481:
1477:
1473:
1457:
1453:
1449:
1445:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1406:Sergei Adian
1399:
1396:
1390:
1386:
1385:, 4), and B(
1382:
1378:
1368:
1362:
1357:, 2) is the
1354:
1347:
1344:cyclic group
1339:
1333:
1327:
1323:
1319:
1315:
1311:
1310:
1304:
1300:
1296:
1292:
1284:
1280:
1276:
1272:
1268:
1264:
1257:
1250:
1246:
1242:
1235:
1228:
1224:
1220:
1216:
1208:
1201:
1197:
1193:
1189:
1182:
1178:
1174:
1170:
1166:
1162:
1155:
1148:
1144:
1140:
1136:
1132:
1128:
1124:
1117:
1110:
1106:
1102:
1098:
1097:, denoted B(
1094:
1090:
1086:
1084:
1078:
1074:
1070:
1066:
1065:
1059:
1056:
1055:, or just a
1052:
1049:
1045:
1041:
1037:
1033:
1029:
1025:
1022:
1017:Cayley graph
1000:
990:
982:Evgeny Golod
979:
973:
969:
965:
964:
956:
951:
947:
943:
939:
931:
929:
916:
907:Sergei Adian
899:
890:
886:
866:
862:
858:
856:
831:Evgeny Golod
823:group theory
815:finite group
802:
800:
629:
617:
605:
593:
581:
569:
557:
545:
316:
273:
260:
249:
238:
234:Cyclic group
112:
99:Free product
70:Group action
33:Group theory
28:Group theory
27:
2219:E. Zelmanov
2163:E. Zelmanov
1946:S. I. Adian
1575:isomorphism
1456:> 1 and
1448:> 1 and
1227:generators
1196:) into the
1147:generators
883:Issai Schur
519:Topological
358:alternating
2286:Categories
1928:2107.09900
1848:References
1601:of finite
950:such that
934:is called
843:restricted
626:Symplectic
566:Orthogonal
523:Lie groups
430:Free group
155:continuous
94:Direct sum
2136:250838960
2017:: 1â308.
1976:: 41â82.
1514:of order
1470:conjugacy
1346:of order
1342:) is the
1330:) finite?
1299:), where
690:Conformal
578:Euclidean
185:nilpotent
2221:(1991).
2211:39623037
2165:(1990).
1894:26 April
1573:, up to
1381:, 3), B(
1089:of rank
1001:a priori
936:periodic
930:A group
685:Poincaré
530:Solenoid
402:Integers
392:Lattices
367:sporadic
362:Lie type
190:solvable
180:dihedral
165:additive
150:infinite
60:Subgroup
2247:Bibcode
2191:Bibcode
2116:Bibcode
1948:(1979)
1838:abelian
1412:number
1371:M. Hall
1283:, then
1256:, ...,
1234:, ...,
1154:, ...,
1116:, ...,
839:bounded
680:Lorentz
602:Unitary
501:Lattice
441:PSL(2,
175:abelian
86:(Semi-)
2209:
2154:
2134:
2072:
1960:
1885:
1673:where
1563:finite
1223:) has
993:-group
959:-group
535:Circle
466:SL(2,
355:cyclic
319:-group
170:cyclic
145:finite
140:simple
124:kernel
2207:S2CID
2132:S2CID
1923:arXiv
1804:Notes
1693:with
1657:with
1603:index
1541:with
1432:â„ 2,
1416:with
1338:B(1,
1291:of B(
1287:is a
1267:with
1188:of B(
1173:) to
1143:with
1077:, is
811:order
719:Sp(â)
716:SU(â)
129:image
2152:ISBN
2070:ISBN
1958:ISBN
1896:2024
1883:ISBN
1557:and
1468:and
1466:word
1404:and
1207:of
1015:The
984:and
905:and
841:and
833:and
801:The
713:O(â)
702:Loop
521:and
2275:at
2255:doi
2231:182
2199:doi
2124:doi
2094:doi
2044:doi
2040:348
2019:doi
1998:doi
1994:289
1978:doi
1974:289
1824:= (
1765:.
1709:)/(
1410:odd
1373:):
1361:of
1249:in
1069:If
1040:in
968:If
942:in
628:Sp(
616:SU(
592:SO(
556:SL(
544:GL(
2288::
2253:.
2243:72
2241:.
2225:.
2205:.
2197:.
2187:36
2185:.
2175:54
2169:.
2130:.
2122:.
2112:60
2110:.
2090:60
2084:.
2064:.
2038:.
2034:.
2015:04
2013:.
1992:.
1834:ba
1832:=
1830:ab
1826:ab
1820:=
1784:,
1749:,
1737:,
1725:,
1669:)/
1649:)/
1645:,
1641:B(
1633:,
1621:,
1613:,
1484:.
1476:,
1440:,
1377:B(
1353:B(
1326:,
1318:,
1295:,
1219:,
1192:,
1169:,
1135:,
1101:,
1044:,
897:.
889:Ă
849:.
604:U(
580:E(
568:O(
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2257::
2249::
2213:.
2201::
2193::
2158:.
2138:.
2126::
2118::
2102:.
2096::
2076:.
2052:.
2046::
2025:.
2021::
2004:.
2000::
1984:.
1980::
1964:.
1931:.
1925::
1898:.
1840:.
1822:b
1818:a
1786:p
1782:m
1780:(
1778:0
1770:p
1763:n
1759:m
1755:n
1751:n
1747:m
1745:(
1743:0
1739:n
1735:m
1733:(
1731:0
1727:n
1723:m
1721:(
1719:0
1715:M
1713:/
1711:N
1707:n
1705:,
1703:m
1701:(
1699:0
1695:m
1691:n
1683:n
1681:,
1679:m
1675:N
1671:N
1667:n
1665:,
1663:m
1659:m
1655:n
1651:M
1647:n
1643:m
1635:n
1631:m
1629:(
1627:0
1623:n
1619:m
1615:n
1611:m
1607:M
1595:n
1591:m
1587:n
1583:m
1577:?
1571:n
1567:m
1559:n
1555:m
1551:G
1547:n
1543:m
1539:G
1516:p
1508:p
1504:p
1482:n
1478:n
1474:m
1458:n
1454:m
1450:n
1446:m
1442:n
1438:m
1434:n
1430:n
1426:m
1422:n
1418:n
1414:n
1393:.
1391:m
1387:m
1383:m
1379:m
1363:m
1355:m
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1348:n
1340:n
1328:n
1324:m
1320:n
1316:m
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1301:m
1297:n
1293:m
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1281:n
1277:G
1273:n
1269:m
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1258:x
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1247:x
1243:x
1238:m
1236:x
1232:1
1229:x
1225:m
1221:n
1217:m
1209:G
1204:i
1202:g
1198:i
1194:n
1190:m
1185:i
1183:x
1179:i
1175:G
1171:n
1167:m
1163:n
1158:m
1156:g
1152:1
1149:g
1145:m
1141:G
1137:n
1133:m
1129:x
1125:x
1120:m
1118:x
1114:1
1111:x
1107:m
1103:n
1099:m
1095:n
1091:m
1079:G
1075:n
1071:G
1060:n
1053:n
1046:g
1042:G
1038:g
1034:n
1030:G
1026:G
991:p
974:G
970:G
957:p
952:g
948:n
944:G
940:g
932:G
891:n
887:n
867:G
863:G
859:G
790:e
783:t
776:v
672:8
670:E
664:7
662:E
656:6
654:E
648:4
646:F
640:2
638:G
632:)
630:n
620:)
618:n
608:)
606:n
596:)
594:n
584:)
582:n
572:)
570:n
560:)
558:n
548:)
546:n
488:)
475:Z
463:)
450:Z
426:)
413:Z
404:(
317:p
282:Q
274:n
271:D
261:n
258:A
250:n
247:S
239:n
236:Z
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