Characterizations of blocks by Loewy lengths of their centers

Otokita, Yoshihiro

doi:10.1090/proc/13529

Characterizations of blocks by Loewy lengths of their centers
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by Yoshihiro Otokita PDF

Proc. Amer. Math. Soc. 145 (2017), 3323-3329 Request permission

Abstract:

We study a block $B$ of a finite group with respect to an algebraically closed field of prime characteristic through the Loewy length $\textrm {ll}{\textbf {Z}B}$ of the center $\textbf {Z}B$. In this paper, we give some upper bounds for $\textrm {ll}{\textbf {Z}B}$ in terms of characters, subsections and defect groups associated to $B$. As a corollary to these results, we characterize some blocks by $\textrm {ll}{\textbf {Z}B}$.

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