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arXiv · 2307.14443

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

Mallika Roy·Enric Ventura
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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 $\mathcal{H}$ of a FATF group $\mathcal{G}$, decides whether $\mathcal{H}$ is the fixed subgroup of some (finite) family of endomorphisms of $\mathcal{G}$ and, in the affirmative case, it finds such a family. The algorithm combines both combinatorial and algebraic methods.

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Mallika Roy, Enric Ventura. 2023-07-26. Computation of endo-fixed closures in free-abelian times free groups. https://arxiv.org/abs/2307.14443

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