Some studies on Loewy lengths of centers of p-blocks

Abstract

In this paper, we investigate some relations between the Loewy lengths of the centers of blocks of group algebras and its defect groups. In particular, we give a new upper bound of the Loewy length and determine the structure of blocks with large Loewy length.

7 pages, Changes from v1: Theorem 1.5 (Theorem 1.5 the case (1) in v1 cannot occur), Proposition 2.5 (4), some typos and minor corrections