Groups with given properties of finite subgroups. (English. Russian original) Zbl 1266.20047

Algebra Logic 51, No. 3, 213-219 (2012); translation from Algebra Logika 51, No. 3, 321-330 (2012).
Summary: Suppose that in every finite even order subgroup \(F\) of a periodic group \(G\), the equality \([u,x]^2=1\) holds for any involution \(u\) of \(F\) and for an arbitrary element \(x\) of \(F\). Then the subgroup \(I\) generated by all involutions in \(G\) is locally finite and is a 2-group. In addition, the normal closure of every subgroup of order 2 in \(G\) is commutative.


20F50 Periodic groups; locally finite groups
20E07 Subgroup theorems; subgroup growth
20E25 Local properties of groups
20F05 Generators, relations, and presentations of groups


Full Text: DOI


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