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Quasigroups having at most three inner mappings. (English) Zbl 0702.20053

The author studies quasigroups with at most three inner mappings. The concluding section describes the Theorem: Let Q be a quasigroup such that Q is not medial and \(i(Q)=3\). Then there exist an abelian group \(Q(+)\), its subgroup B of index 2 and an element \(0\neq w\in B\), \(3w=0\), such that Q is equal to at least one (and then to exactly one) from the quasigroups \(Q(+,B,w,l)\), \(Q(+,B,w,2)\), \(Q(+,B,w,3)\), \(Q(+,B,w,4)\).
Reviewer: C.Pereira da Silva

MSC:

20N05 Loops, quasigroups
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