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Free products of finite groups acting on regular rooted trees. (English) Zbl 1164.20006

Summary: Let a finite number of finite groups be given. Let \(n\) be the largest order of their composition factors. We prove explicitly that the group of finite state automorphisms of the rooted \(n\)-tree contains subgroups isomorphic to the free product of the given groups.

MSC:

20E08 Groups acting on trees
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
57M60 Group actions on manifolds and cell complexes in low dimensions
05C05 Trees
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