On products of Groups with abelian subgroups of small index

2016/11/30 by Amberg, Bernhard, Sysak, Yaroslav
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1611.10093

Abstract

It is proved that every group of the form G=AB with two subgroups A and B each of which is either abelian or has a quasicyclic subgroup of index 2 is soluble of derived length at most 3. In particular, if A is abelian and B is a locally quaternion group, this gives a positive answer to Question 18.95 of "Kourovka notebook" posed by A.I.Sozutov.

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