Faithful homogeneous spaces over commutative groups and TST-spaces.
A set Q is a faithful homogeneous space over a commutative group iff there is a family S of mappings such that (Q,S) is a TST-space.
Laterally commutative heaps and TST-spaces.
A laterally commutative heap can be defined on a given set iff there is the structure of a TST-space on this set.
Hexagonal quasigroups
GS-quasigroups
Symmetries in hexagonal quasigroups
Hexagonal quasigroup is idempotent, medial and semisymmetric quasigroup. In this article we define and study symmetries about a point, segment and ordered triple of points in hexagonal quasigroups. The main results are the theorems on composition of two and three symmetries.
Skewsquares in quadratical quasigroups
The concept of pseudosquare in a general quadratical quasigroup is introduced and connections to some other geometrical concepts are studied. The geometrical presentations of some proved statements are given in the quadratical quasigroup .
Affine regular decagons in GS-quasigroup
In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup .
Subtractive groupoids and TST-spaces
Subtractive groupoids and laterally commutative heaps
Affine regular icosahedron circumscribed around the affine regular octahedron in GS--quasigroup
The concept of the affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be introduced in this paper. The theorem of the unique determination of the affine regular icosahedron by means of its four vertices which satisfy certain conditions will be proved. The connection between affine regular icosahedron and affine regular octahedron in a general GS-quasigroup will be researched. The geometrical representation of the introduced concepts and relations between them...
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