Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups

Simon Goodwin, G Röhrle

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In [S.M. Goodwin, On the conjugacy classes in maximal unipotent subgroups of simple algebraic groups, Transform. Groups 11 (1) (2006) 51-76, 8], the first author outlined an algorithm for calculating a parametrization of the conjugacy Classes in a Sylow p-subgroup U(q) of a finite Chevalley group G(q), valid when q is a power of a good prime for G(q). In this paper we develop this algorithm and discuss an implementation in the computer algebra language GAP. Using the resulting computer program we are able to calculate the parametrization of the conjugacy classes in U(q), when G(q) is of rank at most 6. In these cases, we observe that the number of conjugacy classes of U(q) is given by a polynomial in q with integer coefficients. (C) 2008 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)3321-3334
Number of pages14
JournalJournal of Algebra
Issue number11
Publication statusPublished - 1 Jun 2009


  • Finite Chevalley groups
  • Conjugacy classes
  • Sylow subgroups


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