Totally anti - symmetric quasigroups for all

The spectrum for quasigroups with cyclic automorphisms and additional symmetries

We determine necessary and sufficient conditions for the existence of a quasigroup of order n having an automorphism consisting of a single cycle of length m and n − m fixed points, and having any combination of the additional properties of being idempotent, unipotent, commutative, semi-symmetric or totally symmetric. Quasigroups with such additional properties and symmetries are equivalent to ...

More on embedding partial totally symmetric quasigroups

Evans' Normal Form Theorem Revisited

Evans defined quasigroups equationally, and proved a Normal Form Theorem solving the word problem for free extensions of partial Latin squares. In this paper, quasigroups are redefined as algebras with six basic operations related by triality, manifested as coupled right and left regular actions of the symmetric group on three symbols. Triality leads to considerable simplifications in the proof...

Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

Varieties of P-quasigroups

Decompositions of complete undirected graphs into sets of closed trails which partition the edge set of the graph and which contain each pair of distinct vertices exactly once at distance 2 define and are defined by a class of quasigroups called P-quasigroups. Conditions are established under which P-quasigroups are (or are not) homomorphic images of P-quasigroups which possess certain properti...