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IMCS/Publications/BASM/Issues/BASM n.1 (32), 2000/

Galina Borisovna Belyavskaya. A tribute in honor of her 60th birthday.

Abstract

    On April 19, 2000 Galina Borisovna Belyavskaya, the leading researcher of the Institute of Mathematics and Computer Science of the Academy of Sciences of the Republic of Moldova, a well-known specialist in the field of the theory of quasigroups and combinatorial analysis, Doctor in Physics and Mathematics, celebrated her 60th birthday.
    Galina Borisovna Belyavskaya was born in the town of Ust'-Kamenogorsk of Vest-Kazakhstan region in the family of an engineer. In the middle fifties the family moved to Kishinev. In 1957, after finishing Kishinev secondary school No. 40, she entered the Faculty of Physics and Mathematics of the Kishinev State University and graduated from it with honors in 1962. In the same year Galina Borisovna was employed in just created Institute of Mathematics of the Academy of Sciences of the Republic of Moldova where she has worked till now. Since 1962 she worked at the laboratory of Yu.N.Pecherskii where she elaborated new programming languages, algorithms and packages of applied programs. Since 1967 Galina Borisovna, in the group of V.D.Belousov, began to do investigations in the field of the theory of quasigroups and combinatorial analysis. In 1970 Galina Borisovna defended the candidate thesis "Combinatorial transformations of quasigroups" at the Kishinev State University. In her thesis the new combinatorial concepts of chain isotopy and compression of quasigroups were introduced, the concept of prolongation of quasigroups was generalized. One of the main results of the thesis is a theorem establishing the necessary and sufficient conditions of isotopy of the prolongations of arbitrary admissible quasigroups. The complication of the proof of this theorem is impressive.
    Further Galina Borisovna Belyavskaya was engaged both in algebraic and combinatorial problems of the theory of quasigroups. We would like to mention cycles of works in which she introduced and investigated the concepts of partial admissibility of quasigroups and n-ary quasigroups, partial orthogonality of quasigroups and systems of quasigroups. The cycle of her works on partial orthogonality of quasigroups was highly appreciated by the member of the Academy of Cryptography of Russia M.M.Glukhov, who repeatedly talked about the possibility of application of partially orthogonal quasigroups in cryptography. On the basis of these results Galina Borisovna afterwards wrote a chapter in the monograph of I.Denes and A.D.Keedwell "Latin squares. New Developments in the Theory and Applications", Annals of Discrete Math., vol.46, 1991, North-Holland.
    Galina Borisovna Belyavskaya has introduced and studied two very general methods of construction of quasigroups: using systems of quasigroups and using block-designs. She has found general conditions of the reducibility of an n-ary quasigroup to binary one. Also she investigated the isotopy of A-quasigroups, studied semisymmetric Stein quasigroups, for which she proved that if a semisymmetric Stein quasigroup is isotopic to a group, then this group is abelian. Galina Borisovna carried out the research of S-systems and studied the conditions of closure in k-nets.
    In the beginning of eighties scientific interests of Galina Borisovna shifted to algebraic problems of the theory of quasigroups. She studied the direct decompositions of quasigroups, the concepts of the kernels and centre in quasigroups. A large cycle of her works is devoted to T-quasigroups and quasigroups which are linear or alinear over groups. The characterization of T-quasigroups, linear and alinear quasigroups with the help of identities is one of the most important results in the theory of quasigroups which are linear over groups. Galina Borisovna has introduced and researched the concepts of the commutator and associators in quasigroups. She studied the concept of central isotopy of quasigroups and other problems related to various definitions of the centre of a quasigroup. The last results of Galina Borisovna in the field of the theory of quasigroups are connected with universal-algebraic problems of the theory of quasigroups and also with application of this theory in coding theory.
    Galina Borisovna Belyavskaya has published more than 80 scientific works, among them the monograph "Latin squares, quasigroups and its applications" (co-author V.D.Belousov, Kishinev, "Shtiintsa", 1989). The style of her mathematical works is characterized by completeness in the study of a problem. Galina Borisovna is well known among leading scientists in the field of the theory of quasigroups, and she is personally acquainted with most of them. She gave lectures and talks at many international, All-Union and Republican conferences on algebra and combinatorial theory.
    Galina Borisovna Belyavskaya delivered special lectures on combinatorial analysis at the Kishinev State University, she was an invited professor at the Tashkent Teachers Institute, at Higher Pedagogical Schools of Krakow and Chenstokhov (Poland). For more than 25 years Galina Borisovna has been a reviewer of the Journal of Abstracts (Mathematics), Russia. For more than 20 years Galina Borisovna was the Scientific secretary of the Specialized Council for conferring scientific degree at the Institute of Mathematics of the Academy of Sciences of Moldova. Practically all the persons, who defended the thesis in this Council, recollect Galina Borisovna with the large heat and gratitude for her goodwill and help. in all the problems.
    Galina Borisovna supervised 5 candidate theses. Many scientists from Moldova and other countries were trained under her supervision. She was the scientific adviser of graduate students from the Kishinev State University.
    Since 1971 Galina Borisovna Belyavskaya was the assistant of V.D.Belousov in the sector of the theory of quasigroups; after his death she has headed the research theme on the theory of quasigroups at the Institute of Mathematics of the Academy of Sciences of Moldova, supporting high authority of Belousov's quasigroup school in the world. She is an Advisory Editor of the international journal "Quasigroups and related systems", and also a member of the Editorial Board of the journal "Buletinul Academiei de Stiinte a Republicii Moldova. Matematica". Now Galina Borisovna Belyavskaya is one of the greatest women-mathematicians in Moldova. Galina Borisovna was awarded with State medals.
    Galina Borisovna is kind, sympathetic, delicate, trustworthy, very disciplined, honest and modest woman. She is a good wife, mother and grandmother. She does not love to complain of difficulties and helps the people both word and matter. She is a real spiritual leader.
    We wish Galina Borisovna Belyavskaya strong health, good luck, family well-being, many years of fruitful work and new outstanding results in the theory of quasigroups.