## Illinois Journal of Mathematics

### The automorphism group of a graph product with no SIL

#### 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.

#### Article information

Source
Illinois J. Math., Volume 54, Number 1 (2010), 249-262.

Dates
First available in Project Euclid: 9 March 2011

https://projecteuclid.org/euclid.ijm/1299679748

Digital Object Identifier
doi:10.1215/ijm/1299679748

Mathematical Reviews number (MathSciNet)
MR2776995

Zentralblatt MATH identifier
1243.20047

#### Citation

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

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