Serre’s Property (FA) for automorphism groups of free products

Author:

Andrew Naomi1

Affiliation:

1. School of Mathematical Sciences , University of Southampton , Southampton , SO17 1BJ , United Kingdom

Abstract

Abstract We provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference18 articles.

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2. B. Bekka, P. de la Harpe and A. Valette, Kazhdan’s Property (T), New Math. Monogr. 11, Cambridge University, Cambridge, 2008.

3. O. V. Bogopolskiĭ, Arborial decomposability of groups of automorphisms of free groups, Algebra i Logika 26 (1987), no. 2, 131–149, 271.

4. D. J. Collins and N. D. Gilbert, Structure and torsion in automorphism groups of free products, Quart. J. Math. Oxford Ser. (2) 41 (1990), no. 162, 155–178.

5. Y. Cornulier and A. Kar, On property (FA) for wreath products, J. Group Theory 14 (2011), no. 1, 165–174.

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