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arXiv · 2506.00952

On the class-breadth conjecture

Alexander Skutin
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Abstract

The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that for each $p$-group, $cl(G)\leq b(G) + 1$, where $cl(G)$, $b(G)$ denote the nilpotency class and the breadth of $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p > 2$. This article is dedicated to the general case $p > 2$ of the conjecture.

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Alexander Skutin. 2025-06-01. On the class-breadth conjecture. https://arxiv.org/abs/2506.00952

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