Subloop incompatible Bol loops
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''.
scientific article; zbMATH DE number 5620121
scientific article