Some studies on Loewy lengths of centers of p-blocks

TL;DR

This paper explores the relationships between Loewy lengths of centers of group algebra blocks and their defect groups, providing new bounds and structural insights for blocks with large Loewy lengths.

Contribution

It introduces a new upper bound for Loewy lengths and characterizes the structure of blocks with large Loewy lengths.

Findings

Established a new upper bound for Loewy lengths.

Determined the structure of blocks with large Loewy lengths.

Linked Loewy lengths to properties of defect groups.

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.