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**1 - 1**of**1**### Primitive normal matrices and covering numbers of finite groups

, 2004

"... A primitive matrix is a square matrix M with nonnegative real entries such that the entries of M s are all positive for some positive integer s. The smallest such s is called the primitivity index of M. Primitive matrices of normal type (namely: MM T and M T M have the same zero entries) occur nat ..."

Abstract
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A primitive matrix is a square matrix M with nonnegative real entries such that the entries of M s are all positive for some positive integer s. The smallest such s is called the primitivity index of M. Primitive matrices of normal type (namely: MM T and M T M have the same zero entries) occur naturally in studying the so called ”conjugacy-class covering number ” and ”character covering number” of a finite group. We show that if M is a primitive n n matrix of normal type with minimal polynomial of degree m, then the primitivity index of n M is at most + 1 (m 1). This bound is then applied to improve known