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

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

2008-01-02

arxiv.org/abs/0801.0396v3

Mathematics

Group Theory

14 pages: Significant revisions and explanations expanded

Scientific paper

In earlier work, 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 {\sf 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.

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