--quasigroups.
Generalized distributivity equation on GD-groupoids
Generalized entropy on GD-groupoids with applications to quasigroups of various arities
Generalized fuzzy interior ideals in Abel-Grassmann's groupoids.
Generalized graph cordiality
Hovey introduced A-cordial labelings in [4] as a simultaneous generalization of cordial and harmonious labelings. If A is an abelian group, then a labeling f: V(G) → A of the vertices of some graph G induces an edge-labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. Research on A-cordiality...
Generalized morphisms of abelian m-ary groups
We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.
Generalized Weisner designs and quasigroups.
Generating quasigroups for cryptographic applications
A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of...
Geodesic loops.
Geometric hyperquasigroups and line spaces
Global left loop structures on spheres
On the unit sphere in a real Hilbert space , we derive a binary operation such that is a power-associative Kikkawa left loop with two-sided identity , i.e., it has the left inverse, automorphic inverse, and properties. The operation is compatible with the symmetric space structure of . is not a loop, and the right translations which fail to be injective are easily characterized. satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....
Golden section quasigroups as special idempotent medial quasigroups
Graphs and associative triples in quasitrivial groupoids
Group and hypergroup operations induced by multivalued functions
Group conjugation has non-trivial LD-identities
We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.
Grouplike Menger algebras.
Groupoïdes résidués et demi-groupes nomaux
Groupoids and the associative law I. (Associative triples)
Groupoids and the associative law II. (Groupoids with small semigroup distance)
Groupoids and the associative law III. (Szász-Hájek groupoids)