Ezra Brown

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1. INTRODUCTION. The groups of invertible matrices over finite fields are among the first groups we meet in a beginning course in modern algebra. Eventually, we find out about simple groups and that the unique simple group of order 168 has two representations as a group of matrices. And this is where we learn that the group of 2 × 2 unimodular matrices over(More)
Let A be a k × k matrix over a ring R; let GM (A, R) be the digraph with vertex set R k , and an arc from v to w if and only if w = Av. In this paper, we determine the numbers and lengths of the cycles of GM (A, R) for k = 2 in the following two cases. (a) R = F F q , the q–element finite field, and (b) R = Z Z/nZ Z and GCD(n, det(A)) = 1. This extends(More)
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