Self-invariant \(1\)-factorizations of complete graphs and finite Bol loops of exponent \(2\).
type: Item
instance of: scholarly article
title: Self-invariant \(1\)-factorizations of complete graphs and finite Bol loops of exponent \(2\).
zbMATH Open document ID: 1208.20064
author: Barbara Baumeister
author: Alexander Stein
published in: Beiträge zur Algebra und Geometrie
publication date: 2010-02-09T00:00:00Z
full work available at URL: https://eudml.org/doc/232267
full work available at URL: 9.html
review text: An example of a not soluble finite simple Bol loop of exponent 2 is presented and investigated. This example is called the Aschbacher loop \(A\). \(A\) is a simple loop of order 96 with automorphism group of size 80. This theorem implies the following result: Let \(\Omega\) be a complete graph on 96 vertices and assume that \(K\) is a 1-factorization of \(\Omega\). Put \(G_K=\langle K\rangle\). Then there exists a self-invariant factorization of \(\Omega\) such that \(G_K\) is a non-split extension \(2^{5\cdot}\text{PGL}_2(5)\). Moreover, it is shown: If \(B\) is a finite Bol loop of exponent 2 which is not isomorphic to \(A\) and which is not soluble, then \(|A|<|B|\).
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 5668349
zbMATH Keywords: finite Bol loops
zbMATH Keywords: Moufang loops
zbMATH Keywords: soluble loops
zbMATH Keywords: normal subloops
zbMATH Keywords: sections
zbMATH Keywords: simple loops
zbMATH Keywords: 1-factorizations
zbMATH Keywords: self-invariant factorizations
zbMATH Keywords: complete graphs
reviewed by: Huberta Lausch
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5668349