To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov
On May 11, 2012, we celebrate the 100th anniversary of the birth of Sergei Nikolaevich Chernikov (1912 – 1987), a great mathematician, one of the main founders of infinite group theory.
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
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| Schriftenreihe: | Algebra and Discrete Mathematics |
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| Zitieren: | To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — англ. |
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irk-123456789-1584402019-09-02T01:25:24Z To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov On May 11, 2012, we celebrate the 100th anniversary of the birth of Sergei Nikolaevich Chernikov (1912 – 1987), a great mathematician, one of the main founders of infinite group theory. 2012 Article To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — англ. 1726-3255 http://dspace.nbuv.gov.ua/handle/123456789/158440 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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On May 11, 2012, we celebrate the 100th anniversary of the birth of Sergei Nikolaevich Chernikov (1912 – 1987), a great mathematician, one of the main founders of infinite group theory. |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov Algebra and Discrete Mathematics |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov |
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to the 100th anniversary of the birth of sergei nikolaevich chernikov |
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Інститут прикладної математики і механіки НАН України |
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2012 |
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To the 100th anniversary of the birth of Sergei Nikolaevich Chernikov // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — англ. |
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Algebra and Discrete Mathematics |
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2025-07-14T11:01:14Z |
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2025-07-14T11:01:14Z |
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To the 100th anniversary of the birth of
Sergei Nikolaevich Chernikov
On May 11, 2012, we celebrate the 100th anniversary of the birth of
Sergei Nikolaevich Chernikov (1912 – 1987), a great mathematician, one
of the main founders of infinite group theory.
Sergey N. Chernikov was born in Sergiev–Posad, Moscow Region, into
a Russian orthodox priest’s family. He mentioned a significant influence
his father had on his moral development and his mindset formation.
In 1928, just after graduation from
high school, S. Chernikov began to teach
mathematics at a secondary school. In
1930, he became an external student of
Physics and Technical School at the Sara-
tov Pedagogical Institute. In 1933, after
graduation from the institute, Chernikov
moved to Sverdlovsk (now Yekaterin-
burg). He began his career there as an in-
structor at the mathematics department
of Ural Physics and Mechanics Institute,
and later – Ural Industrial Institute. By
1936, strongly impressed with works of
Dmitri A. Grave and Otto Yu. Schmidt,
which he studied independently, he de-
veloped a great interest in the recent de-
velopments in algebra. At that time he
began intense studies of group theory. These interests naturally brought
him to Moscow University, where he started research work as an external
student under Alexander G. Kurosh’s supervision that lasted from 1936
to 1939. It should be noted that pursuing a scientist’s career was rather
difficult for a priest’s son in that politically difficult time. Perhaps, this
explains why young Chernikov studied mathematics mostly independently.
D 100th anniversary of the birth of S. N. Chernikov
These years can be characterized as a time of rapid development of
investigations in group theory in the USSR. By that time, finite group
theory was quite formed as an intensely developing branch of algebra.
Moreover, some distinct mathematics branches such as geometry, topology,
automorphic function theory, and others began facing problems while
dealing with distinct infinite groups, for some of which the methods of finite
group theory turned out just not applicable. The task of developing general
group theory including as an important part infinite group theory became
imperative. This task has been accomplished concurrently by Soviet and
German mathematicians. German group theory has a great example – well
developed ring theory where the infiniteness was not an obstacle. It’s worth
mentioning that in that time the relations between German and Soviet
mathematicians were very close and fruitful. In particular, the founder of
the Russian (and later the Soviet) group theory school O.Yu. Schmidt and
the teacher of A.G. Kurosch, P.S. Alexandrov, enjoyed very intense and
well-developed personal relationships with German mathematicians and
visited Germany very often. Many German prominent mathematicians,
(in particular, one of the founders of modern algebra Emmy Noether)
delivered their lectures at Moscow State University. This, for the most
part, caused the fact that the finiteness conditions became the main tool in
infinite group theory. The development of this route was enthusiastically
supported by O.Yu. Schmidt, who was conducting the famous seminar at
Moscow State University, and by A.G. Kurosh, who was then studying
topological groups. O.Yu. Schmidt’s algebraic seminar was the main
research center at that time. It attracted many young researchers. The
program of this seminar was in complete harmony with the interests
of young Sergei Chernikov, and he obtained many important results in
a short time. In January 1939, S. Chernikov defended his Ph.D. thesis at
the Algebra Department of Moscow State University. In September 1939,
he was appointed the Chair of Mathematics Department of Ural Industrial
Institute. In 1940, he defended his Dr. of Science thesis at Moscow State
University, and in January, 1941 he became a full professor. O.Yu. Schmidt
was one of the reviewers and opponents for S.N. Chernikov doctoral thesis
defense. In his brief but very thoughtful review, Schmidt underlined that
Chernikov became an accomplished master of mathematical constructions.
In 1945, S.N. Chernikov became a professor in Ural State University. In
1951, he was invited to work for Perm State University, where he had
been working up to 1961. During these 10 years of professorship in Perm,
S.N. Chernikov created a large algebraic scientific school over there. In
1961, the Sverdlovsk Branch of the famous Steklov Mathematics Institute
100th anniversary of the birth of S. N. Chernikov E
of the Academy of Sciences of the USSR was founded, and S.N. Chernikov
was invited to head the Algebra Department there. He was working in this
position from 1961 to 1965. During that time, he continued his research
in group theory, but most of his attention was attracted by his second
area of interest: the newly developed linear inequality theory.
In 1965, S.N. Chernikov moved to Kiev at the invitation of
V.M. Glushkov, the founder of the Institute of Cybernetics of the Na-
tional Academy of Sciences of the Ukraine and one of Chernikov’s former
students. Since then and until the end of his life, Chernikov headed the
Department of Algebra at the Institute of Mathematics of Ukrainian
Academy of Sciences. Simultaneously, since 1965, he taught courses of
algebra at the Kiev Pedagogic University. S.N. Chernikov is rightfully
regarded as one of the founders of modern group theory. He dedicated 50
years of his life to intense and fruitful research of infinite groups. He was
one of small circle of researchers who founded infinite group theory, and
he did a lot for the development of such important areas theory as the
groups with the finiteness conditions and the groups with restrictions on
distinct subgroup families. He introduced numerous global imperative
concepts in group theory such as series of subgroups and distinct classes
of groups defined by these series (so-called Kurosh – Chernikov classes);
he discovered many local properties that occurred to be very effective and
useful; he proposed many new key fruitful ideas and formulated a number
of important problems, some of which are still open by now.
S.N. Chernikov obtained many fundamental results which are rec-
ognized as classical. His ideas influenced works of many prominent
algebraists, such as O. Yu. Shmidt, V.M. Glushkov, B.I. Plotkin,
M.I. Karhapolov, V.S. Charin, I.I. Eremin, Yu.I. Merzlyakov, Yu.M. Gor-
chakov, V.P. Shunkov, D.I. Zaitsev, R. Baer, P. Hall, B.H. Neumann,
B. Hartley, O.H. Kegel, H. Heineken, B.A.F. Wehrfritz, D.J.S. Robinson,
J. Wiegold, J.S. Wilson, and many others.
Sergey N. Chernikov was one of the pioneers in linear programming
and the founder of the algebraic theory of linear inequalities. During WW
II, he actively participated in solving important military-related applied
problems. This activity led him to introducing and developing the so-
called principle of boundary solutions, on whose basis he later constructed
a systematically developed theory of linear inequalities. The method of
convolution of systems of linear inequalities, developed by S.N. Chernikov,
became an important theoretical tool in applied investigations. This
method, in particular, provides a way to study incompatible systems of
linear inequalities, to develop optimization methods for problems with
F 100th anniversary of the birth of S. N. Chernikov
incompatible systems of restrictions, and to give a constructive description
of the entire set of optimal solutions in problems of linear programming.
These results found important continuations in the methods for pattern
recognition developed by I.I. Eremin and his school. S.N. Chernikov dis-
tinguished and studied a key class of infinite systems of linear inequalities,
namely polyhedrally – closed systems, and developed a duality theory
for them. This class of systems serves as a basis for the theoretical and
numerical analysis of nonlinear optimization problems using the reduc-
tion of these problems to problems of semi-infinite and infinite linear
programming.
Being completely dedicated to his research activities, Prof. Chernikov
also devoted much time to disseminating his knowledge and raising
new generation of researchers. He passed his absolute love and dedi-
cation to mathematics to his numerous students. He founded the famous
Chernikov’s group theory school. This school includes more than 50 of his
former Ph.D students; one can find among them such prominent scientists
as V.M. Glushkov, M.I. Kargapolov, I.I. Eremin, and others.
A brilliant lecturer, S.N. Chernikov was able to introduce his audi-
ence in an atmosphere of immediate scientific exploration and discovery.
He constantly encouraged students’ curiosity and interest for research. He
was always ready to answer student questions and never counted hours
he spent on discussing mathematics problems with them. His student will
never forget that.
These days, remembering Sergey Nikolayevich Chernikov as great
scientists and exceptionally wise and caring teacher, the mathematics
community expresses its sincere gratitude for everything that was done
by him in mathematics and education. His brilliant results found their
prominent place in algebra.
Yu. A. Drozd, V. V. Kirichenko,
L. A. Kurdachenko, F. M. Lyman,
M. O. Perestyuk, A. P. Petravchuk,
A. M. Samoilenko, M. M. Semko,
L. A. Shemetkov, I. Ya. Subbotin,
V. I. Sushchansky, V. V. Sharko
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