Schreier loops
We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.
Secure two-way on-line communication by using quasigroup enciphering with almost public key.
Selfdistributive groupoids of small orders
After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.
Selfdistributive groupoids. Part A1. Non-indempotent left distributive groupoids
Selfdistributive groupoids. Part D1: Left distributive semigroups
Selfdistributive grupoids, Part A2: Non-idempotent left distributive quasigroups
Self-invariant 1-factorizations of complete graphs and finite Bol loops of exponent 2.
Self-orthogonal cyclic n-quasigroups.
Self-orthogonal cyclic n-quasigroups. (Short Communication).
Semigroup representations of medial groupoids
Semi-ipergruppi e ipergruppi -completi
Semisymmetrization and Mendelsohn quasigroups
The semisymmetrization of an arbitrary quasigroup builds a semisymmetric quasigroup structure on the cube of the underlying set of the quasigroup. It serves to reduce homotopies to homomorphisms. An alternative semisymmetrization on the square of the underlying set was recently introduced by A. Krapež and Z. Petrić. Their construction in fact yields a Mendelsohn quasigroup, which is idempotent as well as semisymmetric. We describe it as the Mendelsohnization of the original quasigroup. For quasigroups...
Separable Quasigroups.
Several aspects on the hypergroups associated with -ary relations.
Simple balanced groupoids
Simple paramedial groupoids
Simple quasigroups whose inner permutations commute
Simple quasigroups with commuting inner permutations are medial.
Simple zeropotent paramedial groupoids are balanced
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .
Skeletons in multigraphs
Under a multigraph it is meant in this paper a general incidence structure with finitely many points and blocks such that there are at least two blocks through any point and also at least two points on any block. Using submultigraphs with saturated points there are defined generating point sets, point bases and point skeletons. The main result is that the complement to any basis (skeleton) is a skeleton (basis).
Skew elements in -semigroups.