Centralizers and conjugacy classes in finite classical groups

Abstract

Let $\mathcal{C}$ be a classical group defined over a finite field. We present comprehensive theoretical solutions to the following closely related problems: 1) List a representative for each conjugacy class of $\mathcal{C}$. 2) Given $x\in \mathcal{C}$, describe the centralizer $C_{\mathcal{C}}(x)$ of $x$ in $\mathcal{C}$, by giving its group structure and a generating set. 3) Given $x,y\in \mathcal{C}$, establish whether $x$ and $y$ are conjugate in $\mathcal{C}$ and, if they are, find explicit $z\in \mathcal{C}$ such that $z^{-1}xz=y$. We also formulate practical algorithms to solve these problems and have implemented them in Magma.

77 pages, 0 figures, part of PhD thesis under the supervision of Jianbei An and Eamonn O'Brien

References in corpus (1)

• Pairs of Generators for Matrix Groups. I