Browsing by Author "Syrbu, Parascovia"

Browsing by Author "Syrbu, Parascovia"

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  • COMMUTANTS OF MIDDLE BOL LOOPS 
    Grecu, Ion; Syrbu, Parascovia (Academy of Sciences of Moldova, 2014)
    The commutant of a loop is the set of all its elements that commute with each element of the loop. It is known that the commutant of a left or right Bol loop is not a subloop in general. Below we prove that the commutant ...
  • LOOPS WITH INVARIANT FLEXIBILITY UNDER THE ISOSTROPHY 
    Syrbu, Parascovia; Grecu, Ion (Institutul de Matematică şi Informatică al AŞM, 2020)
    The question ”Are the loops with universal (i.e. invariant under the isotopy of loops) flexibility law xy·x=x·yx , middle Bol loops?” is open in the theory of loops. If this conjecture is true then the loops for which ...
  • MIDDLE BRUCK LOOPS AND THE TOTAL MULTIPLICATION GROUP 
    Drapal, Ales; Syrbu, Parascovia (Springer, 2022)
    Let Q be a loop. The mappings x↦ ax, x↦ xa and x↦ a/ x are denoted by La, Ra and Da, respectively. The loop is said to be middle Bruck if for all a, b∈ Q there exists c∈ Q such that DaDbDa= Dc. The right inverse of Q is ...
  • ON A GENERALIZATION OF THE INNER MAPPING GROUP 
    Syrbu, Parascovia (CEP USM, 2017)
    We consider the group GM(Q,·), generated by all left, rightand middle translations of a loop (Q,·). The generalized innermapping groupJ consists of all mappingsα∈GM(Q,·), such that α(e) =e, wheree is the unit of (Q,·). In ...
  • ON INVARIANCE OF RECURSIVE DIFFERENTIABILITY UNDER TH E ISOTOPY OF LEFT BOL LOOPS 
    Larionova-Cojocaru, Inga; Syrbu, Parascovia (CEP USM, 2007)
    We prove that the recursive derivatives of order 1 of isotopic left Bol loops are isotopic and that every loop, isotopic to a recursively 1-differentiable left Bol loop, is recursively 1-differentiable.The recursive ...
  • ON ORTHOGONAL SYSTEMS OF TERNARY QUASIGROUPS ADMITTING NONTRIVIAL PARATOPIES. 
    Syrbu, Parascovia; Ceban, Dina (Institutul de Matematică şi Informatică al AŞM, 2017)
    In the present workwe describ eallorthogonal systems consisting of three ternary quasigroupop erations and of all (three) ternary selectors,admitting at least one nontrivial paratopy. In[11]we proved that there exist ...
  • ON QUASIGROUPS WITH SOME MINIMAL IDENTITIES 
    Ceban, Dina; Syrbu, Parascovia (CEP USM, 2015)
    Quasigroups with two identities (of typesT1 and T2) from Belousov-Bennett classification are considered. It is proved that a π-quasigroup of type T2 is also of type only if it satisfies the identity yx∙x=y (the “right keys ...
  • ON RECURSIVE DIFFERENTIABILITY OF BINARY QUASIGROUPS 
    Larionova-Cojocaru, Inga; Syrbu, Parascovia ("VALINEX", 2014)
    A quasigroup is called recursively n-differentiable if its first n recursive derivatives are quasigroups. The class of recursively differential quasigroups is arisen in the theory of MDS codes, in early 2000. Connections ...
  • ON RECURSIVE DIFFERENTIABILITY OF BINARY QUASIGROUPS 
    Larionova-Cojocaru, Inga; Syrbu, Parascovia (CEP USM, 2015)
    Recursively differentiable binary quasigroups and loops, are considered in the present paper. Invariants under the recursive differentiability of binary quasigroups are found. It is shown that the recursive derivative of ...
  • ON RECURSIVELY DIFFERENTIABLE K-QUASIGROUPS 
    Syrbu, Parascovia; Cuznețov, Elena (2022)
    Recursive differentiability of linear k-quasigroups (k ≥ 2) is studied in the present work. A k-quasigroup is recursively r-differentiable (r is a natu- ral number) if its recursive derivatives of order up to r are ...
  • ON THE HOLOMORPH OF ¼-QUASIGROUPS OF TYPE T1 
    Ceban, Dina; Syrbu, Parascovia ("VALINEX", 2014)
    Quasigroups satisfying the identity x¢(x¢(x¢y)) = y are called ¼-quasigroups of type T1. Necessary and su±cient conditions for the holomorph of a ¼-quasigroup of type T1 to be a ¼-quasigroup of type T1 are established. ...
  • ON π-QUASIGROUPS ISOTOPIC TO ABELIAN GROUPS 
    Syrbu, Parascovia (Institutul de Matematică şi Informatică al AŞM, 2009)
    Aπ-quasigroup is a quasigroup satisfying one of the seven minimalidentities from the V.Belousov’s classification given in [1]. Some general results aboutπ-quasigroups isotopic to groups are obtained by V. Belousovand A. ...
  • ON Π-QUASIGROUPS OF TYPET1 
    Syrbu, Parascovia; Ceban, Dina (Academy of Sciences of Moldova, 2014)
    Quasigroups satisfying the identityx(x· xy ) = y are called π -quasigroups of type T 1 . The spectrum of the defining identity is precisely q = 0 or 1(mod 3), except for q = 6. Necessary conditions when a ...
  • VALENTIN BELOUSOV (20.02.1925 – 23.07.1988) 
    Choban, Mitrofan; Izbash, Vladimir; Şcerbacov, Victor; Syrbu, Parascovia (Institutul de Matematică şi Informatică al AŞM, 2016)