Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups
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The classical result by Dyer–Scott about fixed subgroups of finite order automor-phisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of Bestvina–Handel Theorem: the rank of fixed subgroups of finite order automorphisms is uniformly bounded in terms of m, n. We also studyperiodic points of endomorphisms of Zm×Fn, and give an algorithm to compute auto-fixed closures of finitely generated subgroups of Zm×Fn. On the way, we prove the analog of Day’sTheorem for real elements in Zm×Fn, contributing a modest step into the project of doing sofor any right angled Artin group (as McCool did with respect to Whitehead’s Theorem in the free context).
CitationRoy, M.; Ventura, E. Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups. "Journal of pure and applied algebra", 1 Abril 2020, vol. 224, núm. 4, p. 106210: 1-106210: 19.