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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
##### Keywords:
quasigroups; inner mappings; abelian group
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