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arXiv · 1403.5153

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

Benjamin Sambale
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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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BibTeXRIS

Benjamin Sambale. 2014-03-20. The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups. https://arxiv.org/abs/1403.5153

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