Fixed point ratios in actions of finite classical groups, III

By Timothy C. Burness. 2007

74 citations recorded by the source corpus.

Abstract 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.

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a62d3da13d786ff66797000fe7b57d7006ba2eaa

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In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

In Geometry and Topology

Citations in the corpus

Base sizes for simple groups and a conjecture of Cameron (2009, methodology): “Then proceeding as in the proof of [49, Theorem 1.11], using the bound on fixed point ratios in [ 9, Theorem 1 ], we deduce that”
On base sizes for actions of finite classical groups (2007, background): “The main theorem of [3] states that the Liebeck–Shalev result holds with an explicit constant ≈ 1/2.”