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The symmetries of McCullough-Miller space. (English) Zbl 1288.20033

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 \(n\).

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
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