Title

On Groups with Two Isomorphism Classes of Derived Subgroups

Publication Date

9-2013

Journal

Glasgow Mathematical Journal

Volume

55

Issue

3

First Page

655

Last Page

668

Abstract

The structure of groups which have at most two isomorphism classes of derived subgroups (D-2-groups) is investigated. A complete description of D-2-groups is obtained in the case where the derived subgroup is finite: the solution leads an interesting number theoretic problem. In addition, detailed information is obtained about soluble D-2-groups, especially those with finite rank, where algebraic number fields play an important role. Also, detailed structural information about insoluble D-2-groups is found, and the locally free D-2-groups are characterized.

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