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On the Abelian inner permutation groups of loops. (English) Zbl 0913.20043
The main theorem of this paper is: Let $$Q$$ be a loop such that the inner permutation group $$I(Q)$$ of $$Q$$ is finite and Abelian. Then $$Q$$ is centrally nilpotent and no non-trivial primary $$p$$-component of $$I(Q)$$ is cyclic.
This result is a generalization of previous works of M. Niemenmaa [Commun. Algebra 24, No. 1, 135-142 (1996; Zbl 0853.20049)] and M. Niemenmaa and T. Kepka [Bull. Aust. Math. Soc. 49, No. 1, 121-128 (1994; Zbl 0799.20020)], where a restrictive assumption in addition was that $$Q$$ is a finite loop.

##### MSC:
 20N05 Loops, quasigroups 20B35 Subgroups of symmetric groups
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##### References:
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