Open Access
Spring 2010 The automorphism group of a graph product with no SIL
Ruth Charney, Kim Ruane, Nathaniel Stambaugh, Anna Vijayan
Illinois J. Math. 54(1): 249-262 (Spring 2010). DOI: 10.1215/ijm/1299679748

Abstract

We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphisms generated by partial conjugations is itself a graph product of cyclic groups providing its defining graph does not contain any separating intersection of links (SIL). In the case that all the cyclic groups are finite, this implies that the automorphism group is virtually $\operatorname{CAT}(0)$; it has a finite index subgroup which acts geometrically on a right-angled building.

Citation

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Ruth Charney. Kim Ruane. Nathaniel Stambaugh. Anna Vijayan. "The automorphism group of a graph product with no SIL." Illinois J. Math. 54 (1) 249 - 262, Spring 2010. https://doi.org/10.1215/ijm/1299679748

Information

Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1243.20047
MathSciNet: MR2776995
Digital Object Identifier: 10.1215/ijm/1299679748

Subjects:
Primary: 20F28 , 20F36 , 20F55

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

Vol.54 • No. 1 • Spring 2010
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