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2025-06-03 07:32:26

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

On the class-breadth conjecture
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 one simplified version of the conjecture for $p > 2$.