Embedding partial totally symmetric quasigroups

More on embedding partial totally symmetric quasigroups

Totally anti - symmetric quasigroups for all

A quasigroup (Q, ∗) is called totally anti-symmetric if (c ∗ x) ∗ y = (c ∗ y) ∗ x⇒ x = y and x∗y = y∗x⇒ x = y. A totally anti-symmetric quasigroup can be used for the definition of a check digit system. Ecker and Poch [9] conjectured that there are no totally anti-symmetric quasigroups of order 4k + 2. This article will completely disprove their conjecture (except for n = 2, 6) as we will give ...

Totally geodesic submanifolds in Riemannian symmetric spaces

In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of my classification of the totally geodesic submanifolds in the Riemannian symmetric spaces of rank 2. To appear in the Proceedings volume for the conference V...

Totally nonpositive completions on partial matrices ∗ †

An n × n real matrix is said to be totally nonpositive if every minor is nonpositive. In this paper, we are interested in totally nonpositive completion problems, that is, does a partial totally nonpositive matrix have a totally nonpositive matrix completion? This problem has, in general, a negative answer. Therefore, we analyze the question: for which labeled graphs G does every partial totall...

Quasigroups, right quasigroups and category coverings

The category of modules over a fixed quasigroup in the category of all quasigroups is equivalent to the category of representations of the fundamental groupoid of the Cayley diagram of the quasigroup in the category of abelian groups. The corresponding equivalent category of coverings, and the generalization to the right quasigroup case, are also described.