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Characterizations of blocks by Loewy lengths of their centers


Author: Yoshihiro Otokita
Journal: Proc. Amer. Math. Soc. 145 (2017), 3323-3329
MSC (2010): Primary 20C15, 20C20; Secondary 16S34
DOI: https://doi.org/10.1090/proc/13529
Published electronically: January 31, 2017
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Abstract: We study a block $ B$ of a finite group with respect to an algebraically closed field of prime characteristic through the Loewy length $ {\rm ll}{{\bf Z}B}$ of the center $ {\bf Z}B$. In this paper, we give some upper bounds for $ {\rm ll}{{\bf Z}B}$ in terms of characters, subsections and defect groups associated to $ B$. As a corollary to these results, we characterize some blocks by $ {\rm ll}{{\bf Z}B}$.


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Additional Information

Yoshihiro Otokita
Affiliation: Department of Mathematics and Informatics, Graduate School of Science, Chiba University, 1-33 Yayoi-Cho, Inage-Ku, Chiba-Shi, 263-8522, Japan
Email: otokita@chiba-u.jp

DOI: https://doi.org/10.1090/proc/13529
Keywords: Block, center, Loewy length
Received by editor(s): July 6, 2016
Received by editor(s) in revised form: September 19, 2016
Published electronically: January 31, 2017
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society