The symmetries of McCullough-Miller space

Adam Piggott

The symmetries of McCullough-Miller space

Adam Piggott^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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 group of outer automorphisms of W. We also prove that, for each integer n ≥ 3, the automorphism group of the hypertree complex of rank n is isomorphic to the symmetric group of rank n.

Original language	English
Pages (from-to)	239-266
Number of pages	28
Journal	Algebra and Discrete Mathematics
Volume	14
Issue number	2
Publication status	Published - 2012
Externally published	Yes

Cite this

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title = "The symmetries of McCullough-Miller space",

abstract = "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 group of outer automorphisms of W. We also prove that, for each integer n ≥ 3, the automorphism group of the hypertree complex of rank n is isomorphic to the symmetric group of rank n.",

keywords = "Autmorphisms of groups, Coxeter groups, Group actions on simplicial complexes, Hypertrees, McCullough-Miller space",

author = "Adam Piggott",

year = "2012",

language = "English",

volume = "14",

pages = "239--266",

journal = "Algebra and Discrete Mathematics",

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T1 - The symmetries of McCullough-Miller space

AU - Piggott, Adam

PY - 2012

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N2 - 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 group of outer automorphisms of W. We also prove that, for each integer n ≥ 3, the automorphism group of the hypertree complex of rank n is isomorphic to the symmetric group of rank n.

AB - 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 group of outer automorphisms of W. We also prove that, for each integer n ≥ 3, the automorphism group of the hypertree complex of rank n is isomorphic to the symmetric group of rank n.

KW - Autmorphisms of groups

KW - Coxeter groups

KW - Group actions on simplicial complexes

KW - Hypertrees

KW - McCullough-Miller space

UR - https://www.scopus.com/pages/publications/84873303434

M3 - Article

SN - 1726-3255

VL - 14

SP - 239

EP - 266

JO - Algebra and Discrete Mathematics

JF - Algebra and Discrete Mathematics

IS - 2

ER -

The symmetries of McCullough-Miller space

Abstract

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