Fixed point ratios in actions of finite classical groups, I

Journal article

This is the first in a series of four papers on fixed point ratios in actions of finite classical groups. Our main result states that if G is a finite almost simple classical group and Ω is a faithful transitive non-subspace G-set then either fpr(x)≲|x^G|^−1/2 for all elements x∈G of prime order, or (G, Ω) is one of a small number of known exceptions. Here fpr(x) denotes the proportion of points in Ω which are fixed by x. In this introductory note we present our results and describe an application to the study of minimal bases for primitive permutation groups. A further application concerning monodromy groups of covers of Riemann surfaces is also outlined.

Authors: Burness, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Algebra
• Volume: 309
• Issue: 1
• Pages: 69-79
• Series: Fixed point ratios in actions of finite classical groups
• Publication date: 2007-03-01
• Edition: Publisher's version
• DOI: 10.1016/j.jalgebra.2006.05.024
• ISSN: 0021-8693
• Language: English
• Keywords: finite classical group; fixed point ratio; primitive permutation group
• Subjects: Mathematics; Group theory and generalizations (mathematics)