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arXiv · 1607.06241

Loewy lengths of centers of blocks

Burkhard Külshammer·Benjamin Sambale
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Abstract

Let B be a block of a finite group with respect to an algebraically closed field F of characteristic p>0. In a recent paper, Otokita gave an upper bound for the Loewy length LL(ZB) of the center ZB of B in terms of a defect group D of B. We refine his methods in order to prove the optimal bound LL(ZB)\le LL(FD) whenever D is abelian. We also improve Otokita's bound for non-abelian defect groups. As an application we classify the blocks B such that LL(ZB)\ge |D|/2.

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BibTeXRIS

Burkhard Külshammer, Benjamin Sambale. 2016-07-21. Loewy lengths of centers of blocks. https://arxiv.org/abs/1607.06241

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