On products of Groups with abelian subgroups of small index

Bernhard Amberg; Yaroslav Sysak

On products of Groups with abelian subgroups of small index

Group Theory 2016-12-01 v1

Authors: Bernhard Amberg , Yaroslav Sysak

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.

Keywords

product of groups abelian subgroups quasicyclic subgroup soluble group derived length locally quaternion group Kourovka notebook

Cite

@article{arxiv.1611.10093,
  title  = {On products of Groups with abelian subgroups of small index},
  author = {Bernhard Amberg and Yaroslav Sysak},
  journal= {arXiv preprint arXiv:1611.10093},
  year   = {2016}
}

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