Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
On π-quasigroups of type T1
Authors: Parascovia Syrbu, Dina Ceban
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Abstract
Quasigroups satisfying the identity $ x(x\cdot xy) = y$ are called $\pi$-quasigroups of type $T_{1}$. The spectrum of the defining identity is precisely $q = 0 \ \text {or} \ 1 (\text {mod}\ 3)$, except for $q = 6$. Necessary conditions when a finite $\pi$-quasigroup of type $T_{1}$ has the order $q = 0\ (\text {mod}\ 3)$, are given. In particular, it is proved that a finite $\pi$-quasigroup of type $T_{1}$ such that the order of its inner mapping group is not divisible by three has a left unit. Necessary and sufficient conditions when the identity $ x(x\cdot xy) = y$ is invariant under the isotopy of quasigroups (loops) are found.State University of Moldova
60 A.Mateevici str., MD-2009 Chishinau
Moldova
E-mail: ,
60 A.Mateevici str., MD-2009 Chishinau
Moldova
E-mail: ,
Fulltext
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Contents
- On a class of weighted composition operators on Fock space
- Invariant Characteristics of Special Compositions in Weyl Spaces WN
- Interpolating Bézier spline curves with local control
- Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions
- On π-quasigroups of type T1
- Irreducible triangulations of the Möbius band
- On 2-primal Ore extensions over Noetherian Weak σ-rigid rings
- Max-Erlang and Min-Erlang power series distributions as two new families of lifetime distribution
- A semi-isometric isomorphism on a ring of matrices
- Compact Global Attractors of Non-Autonomous Gradient-Like Dynamical Systems
- One new class of cubic systems with maximum number of invariant lines omitted in the classification of J. Llibre and N. Vulpe
