Niemenmaa, Markku; Kepka, Tomas On connected transversals to abelian subgroups in finite groups. (English) Zbl 0793.20064 Bull. Lond. Math. Soc. 24, No. 4, 343-346 (1992). The authors continue the study of group-theoretical properties of multiplication groups of loops [begun in J. Algebra 135, No. 1, 112-122 (1990; Zbl 0706.20046)]. Applying the results to loop theory they prove that if the inner mapping group of a loop \(Q\) is abelian and of prime power order then \(Q\) is centrally nilpotent. Reviewer: K.Koziol (Katowice) Cited in 1 ReviewCited in 12 Documents MSC: 20N05 Loops, quasigroups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks Keywords:multiplication groups of loops; inner mapping group; centrally nilpotent Citations:Zbl 0706.20046 PDFBibTeX XMLCite \textit{M. Niemenmaa} and \textit{T. Kepka}, Bull. Lond. Math. Soc. 24, No. 4, 343--346 (1992; Zbl 0793.20064) Full Text: DOI