Finite Groups of Local Characteristic p

The P~! Theorem

Journal of Algebra, Volume 292, Issue 2, 15 October 2005, Pages 363-392

Mario Mainardis   Ulrich Meierfrankenfeld   Gemma Parmeggiani   Bernd Stellmacher


In this paper we assume P!,  Q!, gb>1 for P and that there exists two minimal parabolics P1 and P2 containing S such that  Mi:=< P , Pi >  is contained in a local subgroup and Pi does not normalizes P° . We show that p=3 or 5, Mi/Op(Mi) is isomorphic to SL3(p) and Mi has exactly 2 composition factors in Op(Mi), namely two natural modules dual to each other.

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Last Revised 8/23/05