Asymptotic Bounds for the Size of Hom(A,GL_n(q))

Michael Bate, Alec Gullon

Research output: Contribution to journalArticlepeer-review


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 GL_n(q). The size of X(n,q) is a polynomial in q. In this note it is shown that generically this polynomial has degree n^{2(1-a^{-1}) - \epsilon_r} and leading coefficient m_r, where \epsilon_r and m_r are constants depending only on r := n \mod a. We also present an algorithm for explicitly determining these constants.
Original languageEnglish
Pages (from-to)51-61
Number of pages11
JournalGlasgow Mathematical Journal
Issue number1
Early online date14 Mar 2017
Publication statusPublished - 1 Jan 2018

Bibliographical note

© Glasgow Mathematical Journal Trust 2017. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.


  • Finite Groups
  • Counting Homomorphisms
  • Representation Varieties

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