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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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