Finitely Generated Soluble Groups and Their Subgroups

Abstract

We prove that every finitely generated soluble group that is not virtually abelian has a subgroup of one of a small number of types.

Key Words:

• Infinite soluble groups
• Locally virtually abelian groups

2010 Mathematic Subject Classification:

• 20F16

ACKNOWLEDGMENTS

The authors are grateful to the referee for suggesting the use of Laurent polynomials in Section 2, which considerably shortened the argument.

The first author was supported by a Vice-Chancellor's Scholarship from the University of Warwick.

Notes

Communicated by S. Hermiller.