The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups

Sambale, Benjamin

doi:10.1090/S0002-9939-2015-12637-8

The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups
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Proc. Amer. Math. Soc. 143 (2015), 4291-4304 Request permission

Abstract:

We prove the Alperin-McKay Conjecture for all $p$-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order $p$. In the special case $p=3$, we also verify Alperin’s Weight Conjecture for these defect groups. Moreover, in case $p=5$ we do the same for the non-abelian defect groups $C_{25}\rtimes C_{5^n}$. The proofs do not rely on the classification of the finite simple groups.

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