On automorphism groups of free products of finite groups, I: Proper Actions
Abstract
If G is a free product of finite groups, let Aut1(G) denote all (necessarily symmetric) automorphisms of G that do not permute factors in the free product. We show that a McCullough-Miller [D. McCullough and A. Miller, Symmetric Automorphisms of Free Products, Mem. Amer. Math. Soc. 122 (1996), no. 582] and Guti\'errez-Krsti\'c [M. Guti\'errez and S. Krsti\'c, Normal forms for the group of basis-conjugating automorphisms of a free group, International Journal of Algebra and Computation 8 (1998) 631-669] derived (also see Bogley-Krsti\'c [W. Bogley and S. Krsti\'c, String groups and other subgroups of Aut(Fn), preprint] space of pointed trees is an E Aut1(G)-space for these groups.
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