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Finite loops with nilpotent inner mapping groups are centrally nilpotent. (English) Zbl 1167.20039

The purpose of the author is to show: if \(Q\) is a finite loop and \(I(Q)\) is Abelian or a dihedral 2-group, then \(Q\) is a centrally nilpotent loop. An important role in the proof of the author is played by a result of M. Mazur [J. Group Theory 10, No. 2, 195-203 (2007; Zbl 1150.20010)].

MSC:

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

Citations:

Zbl 1150.20010
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References:

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