FIXED POINT SPACES, PRIMITIVE CHARACTER DEGREES AND CONJUGACY CLASS SIZES

Joint with:

I. M. Isaacs , University of Wisconsin
Thomas Michael Keller , Texas State University
Alexander Moretó , Universitat de València

Abstract:

Let V be a nonzero finite dimensional completely reducible FG-module, where F is any field and G is any finite group. Assume that C_V(G)=0 and let p be the smallest prime divisor of G. Then there exists some element g in G such that

dim C_V(g) ≤ 1/p dim V.

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Last Revised 8/25/05