Some problems in number theory that arise from group theory
type: Item
instance of: scholarly article
title: Some problems in number theory that arise from group theory
zbMATH Open document ID: 1181.11008
DOI: 10.5565/PUBLMAT_PJTN05_09
author: Alexander Moretó
published in: Publicacions Matemàtiques
publication date: 2009-06-05T00:00:00Z
full work available at URL: https://eudml.org/doc/41921
full work available at URL: FileName:APJTN05 09.pdf
review text: This is a survey paper on group-theoretic problems which arise in number theory. In particular, the problems are on arithmetical functions and partitions. One of the more palatable open conjectures is that for primes \(p\neq q\), \((q^q-1)/(p-1)\) never divides \((q^p-1)/(q-1)\) to which an affirmative answer would simplify the proof of Feit and Thompson on the solvability of odd order groups.
reviewed by: Richard A. Mollin
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 11A51
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11N56
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11P82
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5562420
zbMATH Keywords: partition
zbMATH Keywords: symmetric groups
zbMATH Keywords: character degree
zbMATH Keywords: irreducible character
zbMATH Keywords: arithmetical function
MaRDI profile type: Publication
OpenAlex ID: W2058651466
description: scientific article; zbMATH DE number 5562420