Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On conjugate sets of quasigroups
Authors: Tatiana Popovich
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Abstract
It is known that the set of conjugates (the conjugate set) of a binary quasigroup can contain 1, 2, 3 or 6 elements. We establish a connection between different pairs of conjugates and describe all six possible conjugate sets, with regard to the equality ("assembling") of conjugates. Four identities which correspond to the equality of a quasigroup to its conjugates are pointed out. Every conjugate set is characterized with the help of these identities. The conditions of the equality of a T-quasigroup to conjugates are established and some examples of T-quasigroups with distinct conjugate sets are given.E-mail:
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Contents
- Transversals in loops. 3. Loop transversals
- Spectra of semimodules
- A Generalization of Hardy-Hilbert's Inequality for Non-homogeneous Kernel
- Topologies on Specg(M)
- Vague Lie Ideals of Lie Algebras
- On conjugate sets of quasigroups
- Categorial aspects of the semireflexivity
- Inclusion Radii for the Zeros of Special Polynomials
- On LCA groups whose rings of continuous endomorphisms have at most two non-trivial closed ideals. I
- Semilattices of r-archimedean subdimonoids
