2007.45: On the minmal parabolic system related to the monster simple group

2007.45: Peter Rowley (2001) On the minmal parabolic system related to the monster simple group. Journal of Combinatorial Theory, Series A, 96 (2). pp. 199-260. ISSN 0097-3165

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DOI: 10.1006/jcta.2001.3175

Abstract

Almost all of the 26 sporadic finite simple groups possess systems of sub- groups which, in several ways, resemble the parabolic systems of the finite simple groups of Lie type. Many of these systems are catalogued in [RSt, RSm]. Those in [RSt] mirror more closely the minimal parabolic systems of a finite simple group of Lie type. In this paper the term minimal parabolic system will be used in a broader sense, to be explained in a moment. Our interest here is in a very particular kind of (generalized) minimal parabolic system, an example of which occurs in the Monster simple group, and the object of this work is to derive ``local'' information about such a minimal parabolic system. In order to state these results we need to intro- duce some definitions and notation.

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