Loewy lengths of centers of blocks and exponents of defect groups

2019/12/19 by Yoshihiro Otokita, Otokita, Yoshihiro
Mathematics · #20C20 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C20

paper · pdf · doi:10.48550/arxiv.1912.09044

8 pages

arxiv created 2019/12/19 · arxiv updated 2019/12/20

Abstract

In this paper we study the Loewy structure of the center ZB of a block of a finite group with respect to an algebraically closed field of prime characteristic. We first state a new method for calculating the Loewy length LL(ZB) of ZB in terms of subsections and lower defect groups. By applying this result we give an upper bound of LL(ZB) which depends on the exponent of a defect group of B for some cases.

Related

• Loewy lengths of centers of blocks
• On centers of blocks with non-cyclic defect groups
• Some studies on Loewy lengths of centers of p-blocks
• Notes on Loewy series of centers of p-blocks
• Loewy lengths of blocks with abelian defect groups