Principal blocks with six ordinary irreducible characters

TL;DR

This paper classifies certain finite groups based on the structure of their principal p-blocks, specifically those with exactly six ordinary irreducible characters, advancing understanding of group representation theory.

Contribution

It provides a classification of Sylow p-subgroups of finite groups with principal p-blocks containing exactly six ordinary irreducible characters.

Findings

Classification of Sylow p-subgroups with six characters

Identification of structural properties of these groups

Extension of known results in block theory

Abstract

We classify Sylow $p$-subgroups of finite groups whose principal $p$-blocks have precisely six ordinary irreducible characters.