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

Gupta, C. K.; Gupta, N. D.; Oliynyk, A. S.

Algebra Discrete Math. 2007, No. 2, 91-103 (2007).

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

Keywords:

finite groups; regular rooted trees; free products; finite state automorphisms