# Morita equivalence classes of blocks with elementary abelian defect groups of order 32

## TL;DR

This paper develops a classification technique for blocks of finite groups and applies it to classify Morita equivalence classes of blocks with elementary abelian defect groups of order 32, confirming a related conjecture.

## Contribution

It introduces a general method for classifying blocks and applies it specifically to blocks with elementary abelian defect groups of order 32, verifying Harada's conjecture.

## Key findings

- Classified Morita equivalence classes for the specified blocks.
- Confirmed Harada's conjecture for these blocks.
- Provided a new technique for block classification.

## Abstract

We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.