A new proof of Belousov's theorem for a special law of quasigroup operations.
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.
Let be a loop such that is square-free and the inner mapping group is nilpotent. We show that is centrally nilpotent of class at most two.
A solvable primitive group with finitely generated abelian stabilizers is finite.
All ordinal numbers with the following property are found: there exists a loop such that its subloops form a chain of ordinal type .
After describing a (general and special) coordinatization of -nets there are found algebraic equivalents for the validity of certain quadrangle configuration conditions in -nets with small degree .