Primitive prime divisor elements in finite classical groups
Abstract
This is an essay about a certain family of elements in the general linear group GL(d,q) called primitive prime divisor elements, or ppd-elements. A classification of the subgroups of GL(d,q) which contain such elements is discussed, and the proportions of ppd-elements in GL(d,q) and the various classical groups are given. This study of ppd-elements was motivated by their importance for the design and analysis of algorithms for computing with matrix groups over finite fields. An algorithm for recognising classical matrix groups, in which ppd-elements play a central role is described.
Keywords
Cite
@article{arxiv.1412.0814,
title = {Primitive prime divisor elements in finite classical groups},
author = {Cheryl E. Praeger},
journal= {arXiv preprint arXiv:1412.0814},
year = {2014}
}
Comments
This is the pre-publication version of a chapter published in the Proceedings of the 1997 Groups St Andrews conference held in Bath. It is an account of a series of three lectures I gave. The document has 22 pages