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On finite commutative loops which are centrally nilpotent. (English) Zbl 1339.20064

If \(Q\) is a loop, \(H\) is the inner mapping group of \(Q\), and \(H\) is abelian, then in many cases \(Q\) has to be centrally nilpotent of class two. The paper shows that this also happens if \(Q\) is commutative and \(H\) is a product of two cyclic groups that are of the same prime power order. The technique of the proof relies upon the concept of connected transversals.

MSC:

20N05 Loops, quasigroups
20D15 Finite nilpotent groups, \(p\)-groups
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