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Construction and properties of \((r,s,t)\)-inverse quasigroups. II. (English) Zbl 1071.20058

Summary: We give a more general set of necessary and sufficient conditions for a \(T\)-quasigroup to be an \((r,s,t)\)-inverse quasigroup than that given in Part I of the paper [ibid. 266, No. 1-3, 275-291 (2003; Zbl 1070.20077)] and show that the constructions given there are special cases of this more general one.
We prove the existence of \((r,s,t)\)-inverse quasigroups for every choice of positive integers \(r,s,t\) and we discuss the existence of properly defined direct products in more detail.
Finally, we show that the left, right and middle \(A\)-nuclei of an \((r,s,t)\)-inverse quasigroup are isomorphic, and in the case of a loop, coincide.

MSC:

20N05 Loops, quasigroups

Citations:

Zbl 1070.20077
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References:

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