2-groups with given properties of finite subgroups

Lytkina D. V.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 4.

Abstract:
A local finiteness is proved of 2-groups, all of whosefinite subgroups (a) are nilpotent of class 2 or (b) belong to a variety defined by the law \([x,y]^2=1\). Besides, it is proved thatthe order of the derived subgroup of a 2-group \(G\) is at most 2 ifthe order of every conjugacy class of every finite subgroup of \(G\)
is at most 2.

Keywords: periodic group, nilpotency, local finiteness.

The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses.