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Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups

Author
Roy, M.; Ventura, E.
Type of activity
Journal article
Journal
Journal of pure and applied algebra
Date of publication
2020-04-01
Volume
224
Number
4
First page
106210: 1
Last page
106210: 19
DOI
10.1016/j.jpaa.2019.106210
Repository
http://hdl.handle.net/2117/184934 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S0022404919302178 Open in new window
Abstract
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...
Citation
Roy, 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.
Keywords
Auto-fixed closure, Automorphism, Fixed subgroup, Free-abelian times free, Periodic subgroup
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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