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

Venue: | JOURNAL OF ALGEBRA |

Citations: | 11 - 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.

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Citation Context .... Theorem 1.1 was motivated by algorithmic considerations. In [KS1] we gave a constructive black box recognition algorithm for the classical simple PRIME POWER GRAPHS FOR GROUPS OF LIE TYPE 3 groups; =-=[KM]-=- does this for the exceptional groups of Lie type. However, in both papers the characteristic of the group was part of the input. Now Theorem 1.1 allows us to compute the characteristic. In Section 5,... |

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