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.

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