2-blocks with abelian defect groups and inertial quotient of prime order

TL;DR

This paper classifies certain 2-blocks with abelian defect groups and prime order inertial quotient, confirming Broué's conjecture for these cases.

Contribution

It provides a complete classification of 2-blocks with abelian defect groups and prime inertial quotient, and proves Broué's conjecture for them.

Findings

Classified all 2-blocks with abelian defect groups and prime inertial quotient.

Proved Broué's abelian defect group conjecture for these blocks.

Abstract

In this paper, we classify all $2$-blocks for which the defect groups are abelian and the inertial quotient has prime order. As a consequence, we prove that Brou\'e's abelian defect group conjecture holds for all blocks under consideration here.