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A note on the finitely generated fixed subgroup property

Autor: Lei, Jialin, Ma, Jiming, Zhang, Qiang

We study when a group of form $G\times\mathbb{Z}^m (m\geq 1)$ has the finitely generated fixed subgroup property of automorphisms ($\rm{FGFP}_a$), by using the BNS-invariant, and provide some partial answers and non-trivial examples.
Comment: 10

Externí odkaz: http://arxiv.org/abs/2405.12824

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Classification of aut-fixed subgroups in free-abelian times surface groups

Autor: Lei, Jialin, Wang, Peng, Zhang, Qiang

In this paper, we are concerned with the direct product $G=\pi_1(\Sigma)\times \Z^k$ for $\Sigma$ a compact orientable surface with negative Euler characteristic, and give a complete classification of its fixed subgroups of automorphisms. As a coroll

Externí odkaz: http://arxiv.org/abs/2309.13540

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Explicit bounds for fixed subgroups of endomorphisms of free products

Autor: Lei, Jialin, Zhang, Qiang

Publikováno v: Journal of Algebra, 633 (2023) 773-787

For an automorphism $\phi$ of a free group $F_n$ of rank $n$, Bestvina and Handel showed that the rank $rk Fix(\phi)$ of the fixed subgroup is not greater than $n$ (the so-called Scott conjecture). Soon after Bestvina and Handel's announcement, their

Externí odkaz: http://arxiv.org/abs/2301.00171

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