Subloop incompatible Bol loops
type: Item
instance of: scholarly article
title: Subloop incompatible Bol loops
zbMATH Open document ID: 1178.22004
author: Ágota Figula
author: Karl Strambach
published in: Manuscripta Mathematica
publication date: 2009-10-23T00:00:00Z
review text: The background of the paper under review is provided by the monograph by \textit{P.T. Nagy} and \textit{K. Strambach} [Loops in group theory and Lie theory. de Gruyter Expositions in Mathematics 35. Berlin: de Gruyter (2002; Zbl 1050.22001)]. One of the aims is to complete the classification of differentiable Bol loops due to \textit{Á. Figula} [Manuscr. Math. 121, No. 3, 367--384 (2006; Zbl 1109.53054)]. The contents of the paper are nicely summarized in the abstract, and therefore we shall partly quote it here: ``Moreover, using the factorization of Lie groups we determine the simple differentiable proper Bol loops \(L\) having the direct product \(G_1\times G_2\) of two groups with simple Lie algebras as the group topologically generated by their left translations such that the stabilizer of the identity element of \(L\) is the direct product \(H_1\times H_2\) with \(H_i<G_i\). Also if \(G_1=G_2=G\) is a simple permutation group containing a sharply transitive subgroup \(A\), then an analogous construction yields a simple proper Bol loop. If \(A\) is cyclic and \(G\) is finite and primitive, then all such loops are classified''.
reviewed by: Daniel Beltiţă
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 5620121
zbMATH Keywords: differentiable Bol loop
zbMATH Keywords: semisimple Lie groups
zbMATH Keywords: Scheerer extension
MaRDI profile type: Publication
full work available at URL: s00229-009-0279-y
OpenAlex ID: W2082898701
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DOI: 10.1007/S00229-009-0279-Y
description: scientific article; zbMATH DE number 5620121