English

Computation of endo-fixed closures in free-abelian times free groups

Group Theory 2023-07-28 v1

Abstract

In this paper, we explore the behaviour of the fixed subgroups of endomorphisms of free-abelian times free (FATF) groups. We exhibit an algorithm which, given a finitely generated subgroup H\mathcal{H} of a FATF group G\mathcal{G}, decides whether H\mathcal{H} is the fixed subgroup of some (finite) family of endomorphisms of G\mathcal{G} and, in the affirmative case, it finds such a family. The algorithm combines both combinatorial and algebraic methods.

Keywords

Cite

@article{arxiv.2307.14443,
  title  = {Computation of endo-fixed closures in free-abelian times free groups},
  author = {Mallika Roy and Enric Ventura},
  journal= {arXiv preprint arXiv:2307.14443},
  year   = {2023}
}