## 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