𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Prime Power Graphs for Groups of Lie Type

✍ Scribed by William M. Kantor; Ákos Seress

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
403 KB
Volume
247
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We associate a weighted graph ⌬ G to each finite simple group G of Lie type.

Ž .

We show that, with an explicit list of exceptions, ⌬ G determines G up to Ž . isomorphism, and for these exceptions, ⌬ G nevertheless determines the characteristic of G.

This result was motivated by algorithmic considerations. We prove that for any finite simple group G of Lie type, input as a black-box group with an oracle to Ž . 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.

📜 SIMILAR VOLUMES

Matrix Generators for Exceptional Groups
Matrix Generators for Exceptional Groups of Lie Type
✍ R.B Howlett; L.J Rylands; D.E Taylor 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 337 KB

This paper gives a uniform method of constructing generators for matrix representations of finite groups of Lie type with particular emphasis on the exceptional groups. The algorithm constructs matrices for the action of root elements on the lowest dimension representation of an associated Lie algeb