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
收藏
页码：161 / 166
页数：6
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