Construction of long root SL(2,q)-subgroups in black box groups

2010/01/19 by Sukru Yalcinkaya, Yalcinkaya, Sukru
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1001.3184

37 pages, submitted to Journal of Algebra

arxiv created 2010/01/19 · arxiv updated 2010/06/14

Abstract

We present a one sided Monte--Carlo algorithm which constructs a long root \sl₂(q)-subgroup in X/O_p(X), where X is a black-box group and X/O_p(X) is a finite simple group of Lie type defined over a field of odd order q=p^k > 3 for some k\geqslant 1. Our algorithm is based on the analysis of the structure of centralizers of involutions and can be viewed as a computational version of Aschbacher's Classical Involution Theorem. We also present an algorithm which determines whether the p-core (or "unipotent radical") O_p(X) of a black-box group X is trivial or not, where X/O_p(X) is a finite simple classical group of odd characteristic p. This answers a well-known question of Babai and Shalev.

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