Centralisers of Involutions in Black Box Groups

2001/10/22 by Alexandre Borovik, Alexandre V. Borovik, Borovik, Alexandre V.
Mathematics · #20P05 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Probability (math.PR) #math.GR #math.PR #msc:20P05

paper · pdf · doi:10.48550/arxiv.math/0110233

13 pp, LaTeX2e, requires packages latexsym, amssymb

arxiv created 2001/10/22 · openalex publication_date 2001/10/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the p-core of a black box group of odd characteristic. This special role of involutions suggest that the theory of black box groups reproduces, at a non-deterministic level, some important features of the classification of finite simple groups.

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