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A character-theory-free characterization of the Mathieu group M12

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Dieter Held  and
Jörg Hrabě de Angelis
Dieter Held
Affiliation:
Fachbereich MathematikUniversität MainzD-6500 Mainz, Federal Republic of Germany
Jörg Hrabě de Angelis
Affiliation:
Fachbereich MathematikUniversität MainzD-6500 Mainz, Federal Republic of Germany
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Abstract

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The known characterization of the Mathieu group M12 by the structure of the centralizer of a 2-central involution is based on the application of the theory of exceptional characters and uses in addition a block theoretic result which asserts that a simple group of order |M12| is isomorphic to M12. The details of the proof of the latter result had never been published. We show here that M12 can be handled in a completely elementary and group theoretical way.

MSC classification

Secondary: 20D05: Finite simple groups and their classification 20D08: Simple groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 2 , October 1990 , pp. 212 - 230
Copyright
Copyright © Australian Mathematical Society 1990

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