## Prime power graphs for groups of Lie type (2002)

Venue: | JOURNAL OF ALGEBRA |

Citations: | 10 - 6 self |

### BibTeX

@ARTICLE{Kantor02primepower,

author = {William M. Kantor and Ákos Seress},

title = {Prime power graphs for groups of Lie type},

journal = {JOURNAL OF ALGEBRA},

year = {2002},

volume = {247},

pages = {370--434}

}

### OpenURL

### Abstract

We associate a weighted graph (G) to each nite simple group G of Lie type. We show that, with an explicit list of exceptions, (G) determines G up to isomorphism, and for these exceptions, (G) nevertheless determines the characteristic of G. This result was motivated by algorithmic considerations. We prove that for any nite simple group G of Lie type, input as a black box group with an oracle to compute the orders of group elements, (G) and the characteristic of G can be computed by a Monte Carlo algorithm in time polynomial in the input length. The characteristic is needed as part of the input in a previous constructive recognition algorithm for G.