Infinite Groups of Finite Period

被引：11

作者：

Mazurov, V. D. ^{[1
,2
]}

Ol'shanskii, A. Yu. ^{[3
]}

Sozutov, A. I. ^{[4
,5
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Vanderbilt Univ, Stevenson Ctr 1326, Nashville, TN 37240 USA

[4] Siberian Fed Univ, Krasnoyarsk 660041, Russia

[5] Reshetnev Siberian State Aerosp Univ, Krasnoyarsk 660037, Russia

来源：

ALGEBRA AND LOGIC | 2015年 / 54卷 / 02期

关键词：

periodic group; periodic product; spectrum of group; recognizability by spectrum; Baire-Suzuki theorem; modular group;

D O I：

10.1007/s10469-015-9335-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that there exist periodic groups containing elements of even order and only trivial normal 2-subgroups, in which every pair of involutions generates a 2-group. This gives a negative answer to Question 11.11a in the Kourovka Notebook. Furthermore, we point out examples of finite simple groups that are recognizable by spectrum in the class of finite groups but not recognizable in the class of all groups.

引用

页码：161 / 166

页数：6

共 50 条

[11] FINITE-GROUPS OF AUTOMORPHISMS OF INFINITE GROUPS .2.
FOURNELLE, TA
JOURNAL OF ALGEBRA, 1983, 80 (01) : 106 - 112
[12] Infinite groups arising from partial presentations of finite groups
Bergman, GM
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1999, 127 : 425 - 439
[13] Second cohomology groups and finite covers of infinite symmetric groups
Evans, David M.
Pastori, Elisabetta
JOURNAL OF ALGEBRA, 2011, 330 (01) : 221 - 233
[14] FINITE-GROUPS OF AUTOMORPHISMS OF INFINITE GROUPS .1.
FOURNELLE, T
JOURNAL OF ALGEBRA, 1981, 70 (01) : 16 - 22
[15] On noncyclic norm of infinite locally finite groups
Lukashova T.D.
Ukrainian Mathematical Journal, 2002, 54 (3) : 421 - 428
[16] Infinite products of finite simple groups II
Thomas, S
JOURNAL OF GROUP THEORY, 1999, 2 (04) : 401 - 434
[17] FINITE TYPE REPRESENTATIONS OF INFINITE SYMMETRIC GROUPS
LIEBERMAN, A
ACTA SCIENTIARUM MATHEMATICARUM, 1976, 38 (1-2): : 113 - 114
[18] FINITE-GROUPS WHICH ARE AUTOMORPHISM-GROUPS OF INFINITE GROUPS ONLY
ZIMMERMAN, J
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1985, 28 (01): : 84 - 90
[19] Infinite groups generated by equilong transformations of period two
Kasner, E
De Cicco, J
AMERICAN JOURNAL OF MATHEMATICS, 1941, 63 : 709 - 725
[20] INFINITE GROUPS WHOSE PROPER QUOTIENT GROUPS ARE FINITE .2.
MCCARTHY, D
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1970, 23 (05) : 767 - &

← 1 2 3 4 5 →