Presentations of finite simple groups: a computational approach

2008/04/09 by Robert M. Guralnick, Guralnick, R. M., William M. Kantor +5 · 1 citation
Computer Science · Engineering · Mathematics · #20D06 #20F05 (Primary) #20J06 (Secondary) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0804.1396

openalex publication_date 2008/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

All nonabelian finite simple groups of rank n over a field of size q, with the possible exception of the Ree groups ²G₂(3^2e+1), have presentations with at most 80 relations and bit-length O(log n +log q). Moreover, A_n and S_n have presentations with 3 generators, 7 relations and bit-length O(log n), while \SL(n,q) has a presentation with 7 generators, 2 5 relations and bit-length O(log n +log q).

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• On Wiegold's conjecture for the small Ree groups

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