Absolute Fourth Moments and Finiteness of Linear Groups

Abstract

Let G be a finite group. Let V be a faithful irreducible complex G-module whose tensor square is nearly irreducible. We answer a question of N. M. Katz by showing that no noncentral element of G has an eigenspace of dimension greater than 7/8 the dimension of V.

Key Words:

• Absolute fourth moment
• Character ratio

Mathematics Subject Classification:

• Primary 20C15
• Secondary 20C33

ACKNOWLEDGMENT

The research of both authors are partially supported by NSA grants.

Notes

Communicated by A. Turull.