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March 2013 On the uniform spread of almost simple linear groups
Timothy C. Burness, Simon Guest
Nagoya Math. J. 209: 35-109 (March 2013). DOI: 10.1215/00277630-1959460


Let G be a finite group, and let k be a nonnegative integer. We say that G has uniform spread k if there exists a fixed conjugacy class C in G with the property that for any k nontrivial elements x1,,xk in G there exists yC such that G=xi,y for all i. Further, the exact uniform spread of G, denoted by u(G), is the largest k such that G has the uniform spread k property. By a theorem of Breuer, Guralnick, and Kantor, u(G)2 for every finite simple group G. Here we consider the uniform spread of almost simple linear groups. Our main theorem states that if G=PSLn(q),g is almost simple, then u(G)2 (unless GS6), and we determine precisely when u(G) tends to infinity as |G| tends to infinity.


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Timothy C. Burness. Simon Guest. "On the uniform spread of almost simple linear groups." Nagoya Math. J. 209 35 - 109, March 2013.


Published: March 2013
First available in Project Euclid: 27 February 2013

zbMATH: 1271.20012
MathSciNet: MR3032138
Digital Object Identifier: 10.1215/00277630-1959460

Primary: 20D06
Secondary: 20E28, 20F05, 20P05

Rights: Copyright © 2013 Editorial Board, Nagoya Mathematical Journal


Vol.209 • March 2013
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