Epimorphism testing with virtually Abelian targets

TL;DR

This paper demonstrates that the epimorphism problem can be effectively solved when the target groups are either virtually cyclic or composed of an Abelian group combined with a finite group, expanding the classes of groups with known solutions.

Contribution

The paper introduces solutions for the epimorphism problem specifically targeting virtually cyclic and certain virtually Abelian groups, which were previously unresolved.

Findings

Epimorphism problem is solvable for virtually cyclic groups.

Epimorphism problem is solvable for groups that are products of Abelian and finite groups.

Expands understanding of epimorphism problem solutions for complex group classes.

Abstract

We show that the epimorphism problem is solvable for targets that are virtually cyclic or a product of an Abelian group and a finite group.