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ASYMPTOTIC BOUNDS FOR THE SIZE OF Hom(A, GLn(q))
Published online by Cambridge University Press: 14 March 2017
Abstract
Fix an arbitrary finite group A of order a, and let X(n, q) denote the set of homomorphisms from A to the finite general linear group GLn(q). The size of X(n, q) is a polynomial in q. In this note, it is shown that generically this polynomial has degree n2(1 – a−1) − εr and leading coefficient mr, where εr and mr are constants depending only on r := n mod a. We also present an algorithm for explicitly determining these constants.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2017