Products of groups which contain abelian subgroups of finite index


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.

DOI Code: 10.1285/i15900932v34n1p23

Keywords: factorized groups; abelian subgroups; soluble groups; dihedral groups

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