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On the Construction of the Finite Simple Groups with a Given Centralizer of a 2-Central Involution

✍ Scribed by Gerhard O. Michler

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 193 KB
Volume: 234
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8549

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✦ Synopsis

dedicated to helmut wielandt on the occasion of his 90th birthday

Let H be a finite group having center Z H of even order. By the classical Brauer-Fowler theorem there can be only finitely many non-isomorphic simple groups G which contain a 2-central involution t for which C G t ∼ = H. In this article we give a deterministic algorithm constructing from the given group H all the finitely many simple groups G having an irreducible p-modular representation M over some finite field F of odd characteristic p > 0 with multiplicity-free semisimple restriction M H to H, if H satisfies certain natural conditions. As an application we obtain a uniform construction method for all the sporadic simple groups G not isomorphic to the smallest Mathieu group M 11 . Furthermore, it provides a permutation representation, and the character table of G.

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