Finitely generated soluble groups and their subgroups

TL;DR

This paper investigates finitely generated soluble groups, showing that non-virtually abelian groups necessarily contain subgroups of specific types, revealing structural constraints within these groups.

Contribution

It establishes that non-virtually abelian finitely generated soluble groups must contain subgroups of certain specified types, advancing understanding of their subgroup structure.

Findings

Non-virtually abelian finitely generated soluble groups contain specific subgroup types.

Structural constraints are identified within these groups.

The results classify possible subgroup configurations.

Abstract

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