Products of groups which contain abelian subgroups of finite index

Authors

  • B. Amberg

DOI:

https://doi.org/10.1285/i15900932v34n1p23

Keywords:

factorized groups, abelian subgroups, soluble groups, dihedral groups

Abstract

It is unknown whether every group G = AB which is the product of of two abelian-by-finite subgroups A and B must always have a soluble or even metabelian subgroup of finite index. Here we deal with the special case of this problem when A and B contain abelian subgroups of "small" index, notably of index at most 2. Some recent results on the solubility of such groups are discussed which depend on special calculations involving involutions.

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Published

02-12-2014

Issue

Volume 34, Issue 1 (2014)

Section

Articoli

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