Blocks with defect group $\mathbb Z_{2^n}\times \mathbb Z_{2^n}\times \mathbb Z_{2^m}$

TL;DR

This paper proves that blocks with a specific type of defect group are Morita equivalent to their Brauer correspondents, extending understanding in modular representation theory of finite groups.

Contribution

It establishes Morita equivalence for blocks with defect groups of the form Z_{2^n}×Z_{2^n}×Z_{2^m}, where n≥2 and m is arbitrary, a new result in block theory.

Findings

Blocks with the specified defect group are Morita equivalent to their Brauer correspondents.

The result applies for all m and for n≥2.

Advances the classification of blocks in modular representation theory.

Abstract

In this paper, we prove that a block with defect group $\mathbb Z_{2^n}\times \mathbb Z_{2^n}\times \mathbb Z_{2^m}$, where $n\geq 2$ and $m$ is arbitrary, is Morita equivalent to its Brauer correspondent.