Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 209 (2013), 35-109.
On the uniform spread of almost simple linear groups
Let be a finite group, and let be a nonnegative integer. We say that has uniform spread if there exists a fixed conjugacy class in with the property that for any nontrivial elements in there exists such that for all . Further, the exact uniform spread of , denoted by , is the largest such that has the uniform spread property. By a theorem of Breuer, Guralnick, and Kantor, for every finite simple group . Here we consider the uniform spread of almost simple linear groups. Our main theorem states that if is almost simple, then (unless ), and we determine precisely when tends to infinity as tends to infinity.
Nagoya Math. J., Volume 209 (2013), 35-109.
First available in Project Euclid: 27 February 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20D06: Simple groups: alternating groups and groups of Lie type [See also 20Gxx]
Secondary: 20E28: Maximal subgroups 20F05: Generators, relations, and presentations 20P05: Probabilistic methods in group theory [See also 60Bxx]
Burness, Timothy C.; Guest, Simon. On the uniform spread of almost simple linear groups. Nagoya Math. J. 209 (2013), 35--109. doi:10.1215/00277630-1959460. https://projecteuclid.org/euclid.nmj/1361976372