Multiplication groups of finite loops that fix at most two points
type: Item
instance of: scholarly article
title: Multiplication groups of finite loops that fix at most two points
zbMATH Open document ID: 0972.20039
author: Aleš Drápal
published in: Journal of Algebra
publication date: 2001-07-22T00:00:00Z
review text: Let \(Q\) be a finite loop (quasigroup with identity), \(L_a(x):=ax\), \(R_a(x):=xa\). A proof is offered that \(Q\) has to be an Abelian group if every permutation of its multiplication group \(\{L_a,R_a\mid a\in Q\}\) has at most two fixed points. An extension to the infinite case is alluded to in the introduction.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 20B05
Mathematics Subject Classification ID: 20K01
zbMATH DE Number: 1563177
zbMATH Keywords: finite loops
zbMATH Keywords: multiplication groups
zbMATH Keywords: permutations
zbMATH Keywords: fixed points
zbMATH Keywords: Abelian groups
zbMATH Keywords: infinite loops
reviewed by: János Aczél
MaRDI profile type: Publication
full work available at URL: jabr.2000.8472
OpenAlex ID: W1972206626
cites work: Multiplication groups of free loops. I
cites work: Multiplication groups of free loops. II
cites work: A Class of Loops Which are Isomorphic to all Loop Isotopes
cites work: Some Special Conjugacy Closed Loops
cites work: Endliche Gruppen I
cites work: On conjugacy classes in finite loops
cites work: On multiplication groups of loops
cites work: On connected transversals in the projective special linear group \(\text{PSL}(2,7)\)
cites work: Quasiprimitivity and quasigroups
cites work: Q4002697
cites work: The group PSL(2,q) is not the multiplication group of a loop
cites work: Finite classical groups and multiplication groups of loops
DOI: 10.1006/JABR.2000.8472
description: scientific article; zbMATH DE number 1563177