Volume 12, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Finiteness of outer automorphism groups of random right-angled {A}rtin groups

Matthew B Day

Algebraic & Geometric Topology 12 (2012) 1553–1583
Abstract

We consider the outer automorphism group Out(AΓ) of the right-angled Artin group AΓ of a random graph Γ on n vertices in the Erdős–Rényi model. We show that the functions n1(log(n) + log(log(n))) and 1 n1(log(n) + log(log(n))) bound the range of edge probability functions for which Out(AΓ) is finite: if the probability of an edge in Γ is strictly between these functions as n grows, then asymptotically Out(AΓ) is almost surely finite, and if the edge probability is strictly outside of both of these functions, then asymptotically Out(AΓ) is almost surely infinite. This sharpens a result of Ruth Charney and Michael Farber.

Keywords
right-angled Artin group, random graph, automorphism group of group
Mathematical Subject Classification 2010
Primary: 05C80, 20E36, 20F28, 20F69
Secondary: 20F05
References
Publication
Received: 21 June 2011
Revised: 10 April 2012
Accepted: 25 April 2012
Published: 15 July 2012
Authors
Matthew B Day
Department of Mathematical Sciences, SCEN 301
University of Arkansas
Fayetteville, AR 72701
USA
http://comp.uark.edu/~matthewd