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The_Quadratic_Conjecture_and_p-groups_of_maximal_class
Abstract
The Quadratic Conjecture for finite p-groups, which is equivalent to the Strong Oliver Conjecture, asserts that if a finite p-group G acts faithfully on an F-module V, then the center Z(G) contains a quadratic element. In this paper, we investigate the structure of maximal class p-groups and establish that they satisfy the Quadratic Conjecture.
Related
- Ideal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomials
- p-class groups in the cyclotomic ℤp-extension of imaginary quadratic fields
- Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups
- On the class-breadth conjecture for p-groups
- Mild p-Class Tower Groups of Imaginary Quadratic Fields
BibTeX
@misc{duan2026thequadraticconjectureandpgroupsofmaximalclass,
title = {{The_Quadratic_Conjecture_and_p-groups_of_maximal_class}},
author = {Jingjing Duan and Lijian An},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34718},
eprint = {2610.34718},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34718},
}
RIS
TY - UNPB
TI - The_Quadratic_Conjecture_and_p-groups_of_maximal_class
AU - Jingjing Duan
AU - Lijian An
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34718
UR - https://arxiv.org/abs/2610.34718
AB - The Quadratic Conjecture for finite p-groups, which is equivalent to the Strong Oliver Conjecture, asserts that if a finite p-group G acts faithfully on an F-module V, then the center Z(G) contains a quadratic element. In this paper, we investigate the structure of maximal class p-groups and establish that they satisfy the Quadratic Conjecture.
ER -