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arXiv · 1611.10093

On products of Groups with abelian subgroups of small index

Bernhard Amberg·Yaroslav Sysak
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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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Bernhard Amberg, Yaroslav Sysak. 2016-11-30. On products of Groups with abelian subgroups of small index. https://arxiv.org/abs/1611.10093

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