Unsolvability of the isomorphism problem for [free abelian]-by-free groups

TL;DR

This paper proves that determining whether two groups are isomorphic is impossible to decide algorithmically for a certain class of groups formed by a free abelian group extended by a free group.

Contribution

It establishes the unsolvability of the isomorphism problem specifically for [free abelian]-by-free groups, a significant class in group theory.

Findings

Isomorphism problem is unsolvable for [free abelian]-by-free groups.

No algorithm can decide isomorphism in this class.

The result extends understanding of algorithmic limitations in group theory.

Abstract

The isomorphism problem for [free abelian]-by-free groups is unsolvable.