# Evgeny Sergeevich Lyapin

### Born: 19 September 1914 in Odessa, Russian Empire (now Ukraine)

Died: 13 January 2005 in St Petersburg, Russia

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**Evgeny Sergeevich Lyapin**'s father was Sergey Evgenyevich Lyapin who was a well respected teacher of mathematics. Evgeny Sergeevich's mother was also a teacher. Because his health was poor, Sergey Evgenyevich, who had been born in St Petersburg, had been sent to Yalta in the Crimea when he was a young boy. He attended the gymnasium in Yalta where he met his future wife, Evgeny Sergeevich's mother, and then he studied mathematics at Novorossiisk University in Odessa. It was in Odessa that Sergey Evgenyevich's son, Evgeny Sergeevich, was born. The family returned to St Petersburg in November 1917 after the second of the two Russian Revolutions of 1917 which placed the Bolsheviks in power.

Evgeny Sergeevich was interested in mathematics, physics, economics and history when at high school. He achieved top grades in all his subjects and, after graduating from the school in 1931, wished to study economics at university. However, the Russian government did not want people with highly educated parents to study economics, but rather they wanted those from the lower social classes. Not accepted for the subject of his first choice, Evgeny Sergeevich decided that he would study history. Again this was not acceptable since it did not fit in with the government policy of having history written from their perspective. His school teachers advised him to join the Komsomol, an organization for young people aged 14 to 28 that was primarily a political organisation for spreading Communist teachings and preparing future members of the Communist Party. This, it was explained to Evgeny Sergeevich, would open doors to him and allow him to study at university. Being a young man of the highest principles, he did not want to follow this route and refused. He was lucky that in the end someone (of the right class and political views) who had been accepted to study mathematics at university, decided to drop out and Evgeny Sergeevich was given the opportunity to study at Leningrad State University.

In 1936 Lyapin graduated from Leningrad State University but continued to undertake research there under the supervision of V A Tartakovskii. In order to provide an income, he taught at the Herzen Pedagogical Institute as an assistant. At this time Lyapin's research was on the theory of groups and he published his first papers on this topic in 1936-37. His first paper studied the automorphism group of a finite group. He was awarded a Candidate Degree (equivalent to a Ph.D.) in 1939 for his dissertation on the decomposition of abelian groups into direct sums of rational groups. He continued his research, working for the degree of Doctor of Science (equivalent to the habilitation) and by 1940 had published seven papers. However, in June 1941, Germany invaded Russia and by September of that year German troops were on the outskirts of Leningrad cutting the city off from the rest of Russia. There was appalling suffering from shortages of supplies. About 660,000 people died in Leningrad during the siege from scurvy and starvation. The exceptionally bitter winter of 1941-42, when temperatures fell to -40° C, was one of extreme hardship. During the siege Lyapin remained in Leningrad but had to give up his mathematical research and contribute to the war effort. This he did by undertaking meteorological research at the Main Geophysical Observatory in Leningrad. The work he did was of remarkable quality, undertaken in the most dire of circumstances while suffering hunger and extreme hardships with German bombs falling around him. For his outstanding work he was made a Professor of Meteorology.

He returned to his mathematical work after the war ended and in 1945 submitted his thesis on algebraic systems with one infinitary operation. In the same year he published Systems with an infinite operation (Russian) which stated some of the results of his investigations. He defended his thesis in 1946 and was awarded the degree of Doctor of Science. In the same year he was appointed to the Chair of Algebra at the Herzen Pedagogical Institute being also appointed as Professor of Algebra at Leningrad State University. Lyapin began to publish papers on semigroups, the first of these appearing in 1947. He was one of the pioneers in this field and he firmly established his leading role with the publication of the monograph

*Semigroups*(Russian) in 1960. E Hewitt reviewed this Russian text and wrote:-

At least three English translations of this monograph have been published.The volume under review is a survey of the algebraic theory of semigroups as of the year1960(topological semigroups are not considered except in the bibliography). As the author points out, semigroups were considered early in the development of the theory of groups, but were put aside because of the inadequacy of the then available algebraic techniques. The author clearly, and perhaps even a little defensively, states his belief in the importance of semigroups, maintaining that while group theory is the abstract form of the theory of one-to-one mappings of a set onto itself, semigroup theory is the abstract form of the theory of single-valued mappings of a set into itself. Analysis, algebra, geometry, and topology being rich in examples of the latter, their abstract theory deserves recognition. With this viewpoint the reviewer is in wholehearted agreement. ... The book does not, of course, contain every known fact about semigroups. It does, however, offer a very complete introduction to the subject, and will be widely used both as a text and a reference.

Lyapin worked extensively on partial groupoids and the results from his many papers were put together to form a monograph written jointly with A E Evseev and published in Russian as

*Partial algebraic actions*in 1991. Danica Jakubiková-Studenovská writes:-

An English translation was published in 1997 under the titleThe aim of this monograph is to survey the main results concerning partial groupoids(i.e., partial algebras with one partial binary operation)and to investigate the relation of this theory to the theory of(complete)groupoids. ... The monograph is very clearly written. The authors have taken care in writing out full proofs throughout the book. Due to a nice didactic conceptual presentation, it can serve as a textbook for students and other readers. At the same time, in view of the wealth of material on partial groupoids(there are more than140references), the monograph will also be of interest as a reference book for specialists in the theory of partial algebras.

*The theory of partial algebraic operations*. H-J Hoehnke writes:-

In [1] many incidents are recalled which give a vivid impression of Lyapin as a person. We encourage the reader to consult [1] which is an excellent article. We will give just a few quotes, the first one to gain an impression of Lyapin as a teacher:-If in the semigroup axioms the associativity law for the binary operation(multiplication)is suppressed, one obtains a binary algebraic structure, which often, e.g. in the present book, is called a(total)groupoid. If, moreover, the multiplication is also allowed to be partial, and that is the main concern of the book, the authors call such an object a partial groupoid or a pargoid. In this restrictive sense, the book can also be considered as an introduction to the theory of partial operations and partial algebras.

Our next quote gives an indication of his character:-Evgeniy Sergeyevich was also known as a remarkable and very successful teacher and mentor. His classes were always full of deep concepts and new ideas expressed in a simple, rigorous, and crisp form. He taught students and their teachers both in Russia and elsewhere. In the sixties he worked in India as a UNESCO expert and helped to prepare clear recommendations for improving education in that country. Also in the sixties, he initiated fundamental changes in curricula of mathematical subjects in Russian pedagogical universities. Their main thrust was in merging various courses into a few big courses and joining them with a high-level course of elementary mathematics.

As a Head of Department he understood how to treat his colleagues:-In the sixties Lyapin was told to join the Communist Party. That would have greatly enhanced his career and he received a transparent hint that, if he complied, he would become Vice President for Research, a prestigious and honorary office. He refused flatly and unambiguously(although that might be dangerous). So when the Academy of Pedagogical Sciences was organized in the USSR and he was nominated as a member, he was rejected, although there were few people as qualified as him. We mention this episode to emphasize his honesty and real decency.

He had many interests outside mathematics:-As head, Lyapin was in permanent contact with the members of his department and was always well-informed about the research and teaching of each of them. Yet, if a faculty member would come to inform him of some negative aspects in the work of a colleague, Lyapin would always stop such conversation demanding that both faculty members meet and discuss the matter between them. This made it impossible for one faculty member to tattle on his colleague. As a result, there were remarkably few feuds or strained relations between faculty in the department. Many visitors to the department noticed the outstandingly good working atmosphere, where members always supported their colleagues and said positive things about them to the visitors. Needless to say, such behavior of the chairman was(and is)unusual in academia.

Lyapin was married to Lydia Ivanovna, who he met when she was a graduate student of his father. They had two children: Larissa became Professor of Russian Literature; Sergey became an applied mathematics whose interests included research in linguistics. Lydia Ivanovna and Evgeny Sergeevich were married for 52 years and it was a great sadness to Lyapin when his wife died. Lyapin lived, however, to see his four grandchildren grow up and he had the joy of seeing two great-grandchildren born.All his life he was involved in sports: table tennis, skiing, but most of all since his student years he loved tennis. ... He was a good chess player, liked card games, and played bridge on a high level. ... Which of his hobbies did he like best? When asked, he always replied: "Reading." He had been reading all his life; he always considered contact with a good book as the supreme pleasure.

**Article by:** *J J O'Connor* and *E F Robertson*

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