Character estimates for finite simple groups and applications
Michael J. Larsen
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
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Abstract
Let be a finite simple group, an irreducible complex character, and an element of . It is often desirable to have upper bounds for in terms of and some measure of the regularity of . This paper reviews what is known in this direction and presents typical applications of such bounds: to proving certain products of conjugacy classes cover , to solving word equations over , and to counting homomorphisms from a Fuchsian group to .