## Abstract

Let U = U(q) be a Sylow p-subgroup of a finite Chevalley group G = G(q). Röhrle and Goodwin in 2009 determined a parameterization of the conjugacy classes of U, for G of small rank when q is a power of a good prime for G. As a consequence they verified that the number k(U) of conjugacy classes of U is given by a polynomial in q with integer coefficients. In the present paper, we consider the case when p is a bad prime for G. Our motivation is to observe how the situation differs between good and bad characteristics. We obtain a parameterization of the conjugacy classes of U, when G has rank less than or equal to 4, and G is not of type F_{4}. In these cases we deduce that k(U) is given by a polynomial in q with integer coefficients; this polynomial is different from the polynomial for good primes.

Original language | English |
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Pages (from-to) | 3245-3258 |

Number of pages | 14 |

Journal | Communications in Algebra |

Volume | 42 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2014 |

## Keywords

- Chevalley groups
- Conjugacy classes
- Sylow p-subgroups

## ASJC Scopus subject areas

- Algebra and Number Theory