Presentations of finite simple groups: A computational approach

R. M. Guralnick; W. M. Kantor; M. Kassabov; A. Lubotzky

doi:10.4171/JEMS/257

Presentations of finite simple groups: A computational approach

R. M. Guralnick, W. M. Kantor, M. Kassabov, A. Lubotzky

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

All finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups ²G₂(q), have presentations with at most 49 relations and bit-length O(log n + log q). Moreover, A_n and S_n have presentations with 3 generators; 7 relations and bitlength O(log n), while SL(n; q) has a presentation with 6 generators, 25 relations and bit-length O(log n + log q).

Original language	English
Pages (from-to)	391-458
Number of pages	68
Journal	Journal of the European Mathematical Society
Volume	13
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/257
State	Published - 2011

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/257

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title = "Presentations of finite simple groups: A computational approach",

abstract = "All finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups 2G2(q), have presentations with at most 49 relations and bit-length O(log n + log q). Moreover, An and Sn have presentations with 3 generators; 7 relations and bitlength O(log n), while SL(n; q) has a presentation with 6 generators, 25 relations and bit-length O(log n + log q).",

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AB - All finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups 2G2(q), have presentations with at most 49 relations and bit-length O(log n + log q). Moreover, An and Sn have presentations with 3 generators; 7 relations and bitlength O(log n), while SL(n; q) has a presentation with 6 generators, 25 relations and bit-length O(log n + log q).

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M3 - مقالة

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Presentations of finite simple groups: A computational approach

Abstract

All Science Journal Classification (ASJC) codes

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