Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Conjugate sets of loops and quasigroups. DC-quasigroups
Authors: Beliavscaia Galina, T. V. 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 investigate loops, $IP$-quasigroups and $T$-quasigroups with distinct conjugate sets described earlier. We study in more detail the quasigroups all conjugates of which are pairwise distinct (shortly, $DC$-quasigroups). The criterion of a $DC$-quasigroup (a $DC$-$IP$-quasigroup, a $DC$-$T$-quasigroup) is given, the existence of $DC$-$T$-quasi\-groups for any order $n\geq 5$, $n\neq 6$, is proved and some examples of $DC$-quasigroups are given.E-mail: ,
Fulltext
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Contents
- Instability of solutions for nonlinear functional differential equations of fifth order with n-deviating arguments
- The stochastic optimal growth problem
- Conjugate sets of loops and quasigroups. DC-quasigroups
- Center problem for cubic systems with a bundle of two invariant straight lines and one invariant conic
- On cyclically-interval edge colorings of trees
- Post-optimal analysis of investment problem with Wald's ordered maximin criteria
- Matrix algorithm for Polling models with PH distribution
- On asymptotic representation of singular solutions of the model elliptic equation near boundary and formulation of singular
- Moment analysis of the telegraph random process
