On the reduction of Alperin's Conjecture to the quasi-simple groups

2010/04/10 by Puig, Lluis
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1004.1703

Abstract

We show that the refinement of Alperin's Conjecture proposed in "Frobenius Categories versus Brauer Blocks", Progress in Math. 274, can be proved by checking that this refinement holds on any central k*-extension of a finite group H containing a normal simple group S with trivial centralizer in H and p'-cyclic quotient H/S. This paper improves our result in [ibidem, Theorem 16.45] and repairs some bad arguments there.

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• Equivariant Alperin-Robinson's Conjecture reduces to almost-simple k*-groups
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• Jordan Decomposition for the Alperin-McKay Conjecture