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Journal of Algebraic Combinatorics

, Volume 27, Issue 1, pp 99–111 | Cite as

Parabolic conjugacy in general linear groups

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Abstract

Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL n (q). We show that the number of P(q)-conjugacy classes in GL n (q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006)

Keywords

General linear group Parabolic subgroups Conjugacy classes 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BirminghamBirminghamUK
  2. 2.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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