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arxiv: 1810.06287 · v1 · pith:HPTHBJJUnew · submitted 2018-10-15 · 🧮 math.GR

Serre's Property FA for automorphism groups of free products

Nils Leder This is my paper
classification 🧮 math.GR
keywords freepropertyautomorphismgroupsserrecasecasescyclic
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We study the automorphism group Aut(G) of a free product G of finite cyclic groups. We investigate the question in which cases Aut(G) has Serre's property FA. In the case of two or three free factors, we prove that Aut(G) does not have property FA. However, if each free factor of G occurs at least four times we show that Aut(G) does have property FA.

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  1. Serre's Property (FA) for automorphism groups of free products

    math.GR 2019-07 unverdicted novelty 6.0

    The automorphism group of a free product of freely indecomposable non-cyclic groups has Serre's Property (FA) under stated necessary and sufficient conditions, with the finite case completely characterized.