Notes to the Feit-Thompson conjecture
type: Item
instance of: scholarly article
title: Notes to the Feit-Thompson conjecture
zbMATH Open document ID: 1228.11005
author: Kaoru Motose
published in: Proceedings of the Japan Academy. Series A
publication date: 2009-04-27T00:00:00Z
review text: The author presents partial solutions to the Feit-Thompson conjecture such that \((q^{p}-1)/(q-1)\) does not divide \((p^{q}-1)/(p-1)\) for distinct primes \(p < q\). He also makes some observations on the Stephens conjecture [\textit{N. M. Stephens}, Math. Comput. 25, 625 (1971; Zbl 0218.10003)]. The motivation comes from a note on p. 1 in [\textit{T. M. Apostol}, Math. Comput. 29, 1--6 (1975; Zbl 0298.12001)] that the proof of this conjecture could greatly simplify the very long proof of the Feit-Thompson theorem that every group of odd order is solvable
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 5547615
zbMATH Keywords: odd order
zbMATH Keywords: cyclotomic polynomials
zbMATH Keywords: Legendre symbol
MaRDI profile type: Publication
full work available at URL: pjaa.85.16
OpenAlex ID: W2025017212
Wikidata QID: Q122932866
cites work: The Resultant of the Cyclotomic Polynomials F m (ax) and F n (bx)
cites work: A SOLVABILITY CRITERION FOR FINITE GROUPS AND SOME CONSEQUENCES
cites work: Solvability of groups of odd order
cites work: Unsolved problems in number theory
cites work: On the Feit-Thompson Conjecture
DOI: 10.3792/PJAA.85.16
description: scientific article; zbMATH DE number 5547615