×

On subgroups, transversals and commutators. (English) Zbl 0862.20023

Campbell, C. M. (ed.) et al., Groups ’93 Galway/St. Andrews’. Proceedings of the international conference, Galway, Ireland, August 1-14, 1993. Volume 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 212, 476-481 (1995).
From the introduction: When \(H\) is a subgroup of a group \(G\) then the natural way to combine \(H\) and \(G\) is to write \(G=AH\) where \(A\) is a left transversal to \(H\) in \(G\). In this survey we shall consider the situation that \(G=AH=BH\) and the left transversals \(A\) and \(B\) are connected by the commutator condition \([A,B]\leq H\). We investigate the solubility of \(G\) as well as the situation in some finite simple groups. The situation and the conditions that we study arise in a natural way from some problems in loop theory and quasigroup theory.
For the entire collection see [Zbl 0839.00022].

MSC:

20E22 Extensions, wreath products, and other compositions of groups
20N05 Loops, quasigroups
20D40 Products of subgroups of abstract finite groups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
PDFBibTeX XMLCite