The_Quadratic_Conjecture_and_p-groups_of_maximal_class

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34718
Primary Topic
Finite Group Theory Research
Type
preprint
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preprint

The_Quadratic_Conjecture_and_p-groups_of_maximal_class

Lijian An, Jingjing Duan
arXiv (Cornell University)
Finite Group Theory Research
preprint

The_Quadratic_Conjecture_and_p-groups_of_maximal_class

Lijian An, Jingjing Duan
preprint en

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.

arXiv (Cornell University)
Finite Group Theory Research
DOIOpen Access PDFOpenAlex
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The_Quadratic_Conjecture_and_p-groups_of_maximal_class — Lijian An, Jingjing Duan · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS