Serre's Property FA for automorphism groups of free products
Nils Leder
TL;DR
This paper investigates when the automorphism group of a free product of finite cyclic groups possesses Serre's property FA, revealing conditions based on the number of free factors.
Contribution
It establishes new criteria for property FA in automorphism groups of free products, especially highlighting the role of the number of factors.
Findings
Aut(G) lacks property FA for two or three free factors.
Aut(G) has property FA if each free factor appears at least four times.
The results depend on the number of free factors in the free product.
Abstract
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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