Abstract

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

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