PreprintCC BY 4.0arXiv
On the class-breadth conjecture for p-groups
Abstract
The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that the nilpotency class of any p-group is at most b(G) + 1, where b(G) = maxg∈ Glogp[G:ZG(g)] denotes the breadth of a group 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.
Related
- Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups
- The_Quadratic_Conjecture_and_p-groups_of_maximal_class
- Mapping class groups are quasicubical
- On the mapping class groups of simply connected smooth 4-manifolds
- Bowen--Franks groups and minus class groups of imaginary abelian fields
BibTeX
@misc{skutin2026classbreadth,
title = {{On the class-breadth conjecture for $p$-groups}},
author = {Alexander Skutin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.13423},
eprint = {2606.13423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.13423},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the class-breadth conjecture for p-groups
AU - Alexander Skutin
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2606.13423
UR - https://arxiv.org/abs/2606.13423
AB - The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that the nilpotency class of any p-group is at most b(G) + 1, where b(G) = max_g∈ Glog_p[G:Z_G(g)] denotes the breadth of a group 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.
ER -