Document Zbl 1290.20064

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On the isotopy structure of elements of the group \(\mathcal P_p(\mathbb Z_n)\). (English) Zbl 1290.20064

J. Niger. Math. Soc. 32, 317-329 (2013).

Summary: Some linear-bivariate polynomials \(p(x,y)=a+bx+cy\) that generate quasigroups over the ring \(\mathbb Z_n\) and which form a group \(\mathcal P_p(\mathbb Z_n)\) which is a subgroup of a monoid \(H_p(\mathbb Z_n)\) are studied. Their isotopy structure (isotopism, autotopism, isomorphism, automorphism) is also studied. Some sufficient conditions based on \(a,b,c\), for the isomorphism, isotopism and equivalence of the generated quasigroups are also deduced.

MSC:

20N05	Loops, quasigroups
20N02	Sets with a single binary operation (groupoids)

Keywords:

linear-bivariate polynomials; quasigroups generated by polynomials

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