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On connected transversals to abelian subgroups in finite groups. (English) Zbl 0793.20064
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.

MSC:
20N05 Loops, quasigroups
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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