On the Frobenius numbers of symmetric groups
type: Item
instance of: scholarly article
title: On the Frobenius numbers of symmetric groups
zbMATH Open document ID: 0961.20023
author: Yugen Takegahara
published in: Journal of Algebra
publication date: 2001-05-28T00:00:00Z
review text: Let \(A\) be a finite Abelian group and \(G\) a finite group. Then \textit{T. Yoshida} [J. Algebra 156, No. 1, 125-156 (1993; Zbl 0827.20033)] proved that \(|\Hom(A,G)|\equiv 0\bmod\gcd(|A|,|G|)\), which is a generalization of a theorem of Frobenius. The author of the present article proves a theorem whose consequence is the above result.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20B30
zbMATH DE Number: 1400107
zbMATH Keywords: Frobenius numbers
zbMATH Keywords: symmetric groups
zbMATH Keywords: finite Abelian groups
zbMATH Keywords: finite groups
zbMATH Keywords: Frobenius theorem
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
full work available at URL: jabr.1999.7992
OpenAlex ID: W2023971601
cites work: A Unimodality Result in the Enumeration of Subgroups of a Finite Abelian Group
cites work: On computing the number of subgroups of a finite Abelian group
cites work: Q3926778
cites work: On Butler's unimodality result
cites work: Über einen Satz von Dey und die Modulgruppe
cites work: \(|\Hom(A,G)|\).
DOI: 10.1006/JABR.1999.7992
description: scientific article; zbMATH DE number 1400107