Centralisers of Involutions in Black Box Groups

Details Centralisers of Involutions in Black Box Groups Centralisers of Involutions in Black Box Groups

2001-10-22

arxiv.org/abs/math/0110233v1

Mathematics

Group Theory

13 pp, LaTeX2e, requires packages latexsym, amssymb

Scientific paper

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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