Piggott, Adam The symmetries of McCullough-Miller space. (English) Zbl 1288.20033 Algebra Discrete Math. 14, No. 2, 239-266 (2012). Summary: We prove that if \(W\) is the free product of at least four groups of order 2, then the automorphism group of the McCullough-Miller space corresponding to \(W\) is isomorphic to the group of outer automorphisms of \(W\). We also prove that, for each integer \(n\geq 3\), the automorphism group of the hypertree complex of rank \(n\) is isomorphic to the symmetric group of rank \(n\). Cited in 1 Document MSC: 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F28 Automorphism groups of groups 20E36 Automorphisms of infinite groups 57M07 Topological methods in group theory 20F29 Representations of groups as automorphism groups of algebraic systems 20F55 Reflection and Coxeter groups (group-theoretic aspects) 05E18 Group actions on combinatorial structures Keywords:free products; Culler-Vogtmann spaces; McCullough-Miller spaces; automorphisms of groups; group actions on simplicial complexes; Coxeter groups; outer automorphisms PDFBibTeX XMLCite \textit{A. Piggott}, Algebra Discrete Math. 14, No. 2, 239--266 (2012; Zbl 1288.20033)