The breadth-degree type of a finite $p$-group

TL;DR

This paper establishes an upper bound on the size of stem p-groups based on their breadth and maximum character degree, advancing understanding of their structural limitations.

Contribution

It introduces a new bound linking the size of stem p-groups to their breadth and character degree, providing a novel structural insight.

Findings

Derived an explicit upper bound for stem p-groups

Connected group size with breadth and character degree

Enhanced classification tools for finite p-groups

Abstract

We determine an upper bound for the size of a stem $p$-group in terms of its breadth and its maximum character degree.