Leonid A. Kurdachenko (dedicated to 70th Birthday)
Leonid A. Kurdachenko is definitely one of the most productive group theorists. His list of publications consists of more than 250 journal articles published in major mathematics journals in many countries including Ukraine, USA, Germany, Great Britain, Italy, Spain, China, Greece, Brazil, Hungary,...
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Інститут прикладної математики і механіки НАН України
2020
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2023-03-03T15:37:18Z 2023-03-03T15:37:18Z 2020 Leonid A. Kurdachenko (dedicated to 70th Birthday) // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. C–H. — англ. 1726-3255 DOI:10.12958/adm1606 https://nasplib.isofts.kiev.ua/handle/123456789/188497 Leonid A. Kurdachenko is definitely one of the most productive group theorists. His list of publications consists of more than 250 journal articles published in major mathematics journals in many countries including Ukraine, USA, Germany, Great Britain, Italy, Spain, China, Greece, Brazil, Hungary, Poland, Czech Republic, Turkey, and Russia. He is an author of more than a dozen of books published by such prestigious publishers as John Wiley & Sons (USA), Birkhäuser (Swiss), World Scientific (United Kingdom), and others. He is a very popular invited speaker and visiting professor in many international conferences and universities, including University of Zaragoza, University of Naples, University of Salerno, University of Alabama, and others. He supervised 9 Ph.D. students and a D.Sc. student who actively work in algebra. His input in the development of Ukrainian algebra is difficult to overestimate. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Leonid A. Kurdachenko (dedicated to 70th Birthday) Article published earlier |
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Leonid A. Kurdachenko is definitely one of the most productive group theorists. His list of publications consists of more than 250 journal articles published in major mathematics journals in many countries including Ukraine, USA, Germany, Great Britain, Italy, Spain, China, Greece, Brazil, Hungary, Poland, Czech Republic, Turkey, and Russia. He is an author of more than a dozen of books published by such prestigious publishers as John Wiley & Sons (USA), Birkhäuser (Swiss), World Scientific (United Kingdom), and others. He is a very popular invited speaker and visiting professor in many international conferences and universities, including University of Zaragoza, University of Naples, University of Salerno, University of Alabama, and others. He supervised 9 Ph.D. students and a D.Sc. student who actively work in algebra. His input in the development of Ukrainian algebra is difficult to overestimate.
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1726-3255 |
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Leonid A. Kurdachenko (dedicated to 70th Birthday) // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. C–H. — англ. |
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“adm-n1” — 2020/5/14 — 19:35 — page C — #3
© Algebra and Discrete Mathematics
Volume 29 (2020). Number 1, pp. C–H
DOI:10.12958/adm1606
Leonid A. Kurdachenko
(dedicated to the 70th birthday)
This special issue of the journal is dedicated to the 70th birthday of an
outstanding Ukrainian mathematician, Professor Leonid A. Kurdachenko.
Leonid A. Kurdachenko is definitely one of the most productive group
theorists. His list of publications consists of more than 250 journal articles
published in major mathematics journals in many countries including
Ukraine, USA, Germany, Great Britain, Italy, Spain, China, Greece, Brazil,
Hungary, Poland, Czech Republic, Turkey, and Russia. He is an author of
https://doi.org/10.12958/adm1606
“adm-n1” — 2020/5/14 — 19:35 — page D — #4
D Leonid A. Kurdachenko
more than a dozen of books published by such prestigious publishers as
John Wiley & Sons (USA), Birkhäuser (Swiss), World Scientific (United
Kingdom), and others. He is a very popular invited speaker and visiting
professor in many international conferences and universities, including
University of Zaragoza, University of Naples, University of Salerno, Univer-
sity of Alabama, and others. He supervised 9 Ph.D. students and a D.Sc.
student who actively work in algebra. His input in the development of
Ukrainian algebra is difficult to overestimate.
Leonid was born on October 22, 1949 in Dnipro. In 1971 he
graduated with the high honors from the Mechanics and Mathematics
School of National Dnipro University. In 1969 Leonid Kurdachenko met
Sergey N. Chernikov and in 1971 he became his postgraduate student.
S. N. Chernikov is known not only as a great mathematician and one of the
founders of infinite group theory, but also as a very influential and caring
teacher. It is worthy to mention that among his numerous students we can
list such prominent mathematicians as V. M. Glushkov, M. I. Kargapolov,
V. S. Charin, V. P. Shunkov, Yu. I. Gorchakov, D. I. Zaitsev, and others.
In 1974 Leonid Kurdachenko was awarded a Ph.D. degree and began
his career as an assistant professor at the Department of Algebra and
Geometry of National Dnipro University. In 1976 he became an associate
professor, and in 1977 the Department Chair. In 1992 Leonid Kurdachenko
defended his Doctor of Sciences thesis at St Petersburg University. He has
been also awarded a Doctor of Sciences Degree by Kiev University. Since
1996 Leonid Kurdachenko is a Full Professor and Chair of the Department
of Algebra and Geometry of National Dnipro University. In 1998 he was
awarded by an honorary title Distinguished Scientist of Ukraine.
Leonid Kurdachenko is a world class expert and lead researcher in al-
gebra. His areas of research where he made an outstanding, and sometime
foundational inputs, includes, but not limited, with the following topics:
restrictions on conjugacy classes (FC-groups and their generalizations);
weak minimal and weak maximal condition on some family of subgroups;
modules over group rings and linear groups; restrictions on factor-groups;
restrictions on generalized normal subgroups; rank and section p-rank; an-
“adm-n1” — 2020/5/14 — 19:35 — page E — #5
Dedicated to the 70th birthday E
tipodes to normal subgroups and transitivity of some subgroup properties;
the Schur theorem and related results; fuzzy groups (classical algebraic
approach); Leibniz algebras (in the spirit of applying group theoretical
methods).
Initially, the theory of FC-groups was developed in the frame of periodic
groups. L. A. Kurdachenko showed that non-periodic FC-groups have their
own nature, which is different from that of periodic FC-group. He obtained
the first important results on non-periodic FC-groups and developed the
foundation for their theory. In collaboration with M. Tomkinson and
J. Otal, Leonid Kurdachenko continued deep studies of periodic FC-groups
and obtained important results about their structure. A key role in the
design and formation of topics related to the study of groups by the
properties of classes of conjugate elements belongs to him.
One of the mainstreams in group theory (both infinite and finite)
is the study of the influence of systems of subgroups on the structure
of a group. L. A. Kurdachenko’s significant input in this area is well-
known. Inspired by D. I. Zaitsev, he successfully continued the initiated by
R. Baer and D. I. Zaitsev study of groups with weak minimal and maximal
conditions. L. A. Kurdachenko wrote a series of articles on groups with
weak minimal and maximal conditions on normal subgroups. Together
with V.E. Goretskii, G. Cutolo, H. Smith, I. Ya. Subbotin, L. S. Kazarin,
P. Shumyatskii and others, he investigates groups with weak maximal and
minimal conditions on different important families of subgroups.
Investigation of groups satisfying some conditions related to the sub-
group arrangement allowed algebraists to introduce and describe many
important classes of groups. The roots of such investigations lie in the
works of P. Hall, R. Carter, J. Rose, and Z. Borevich. Lately, numerous
interesting results in this area have been obtained by many authors. In
collaboration with I. Ya. Subbotin, J. Otal, G. Vincenzi, A. Russo and
others, L. A. Kurdachenko was able to discover some important prop-
erties of pronormal, Carter, abnormal, and contranormal subgroups of
infinite groups and investigate their influence on the groups structure.
Lately, together with A. Ballester-Bolinches and T. Pedraza, L. A. Kur-
“adm-n1” — 2020/5/14 — 19:35 — page F — #6
F Leonid A. Kurdachenko
dachenko published a cycle of interesting articles dedicated to properties
of permutable and Sylow permutable subgroups in infinite periodic groups.
The studies related to weak minimal conditions led L. A. Kurdachenko
to the theory of modules over group rings. Some types of modules that
were investigated by L. A. Kurdachenko, are proved to be useful in the
studies of the influence of factor-groups on the structure of the group. In
collaboration with I. Ya. Subbotin and J. Otal, L. A. Kurdachenko was
able to make a significant input in this theory. It was reflected in the book
of L. A. Kurdachenko, J. Otal, I. Ya. Subbotin Groups With Prescribed
Quotient Groups and Associated Module Theory, World Scientific, New
Jersey, London, Singapore, Hong Kong, 2002.
Research activities of L. A. Kurdachenko in the theory of modules
were not only limited to those that have applications to group theory. On
the contrary, he, along with other algebraists, ensured that the theory of
modules over group rings ceases to be an application, but finds its own
theme. This was largely facilitated in the book by L. A. Kurdachenko,
J. Otal, I. Ya. Subbotin Artinian Modules Over Group Ring, Series Frontiers
in Mathematics, Birkhäuser, Basel, 2007.
The theory of modules over group rings is closely related to the theory
of linear groups. Some of its problems led to the need of study linear
groups over vector spaces of infinite dimension. Theory of finite-dimensional
linear groups, i.e., subgroups of the group GL(F,A) where A is a finite-
dimensional vector space over a field F , is one of the best developed
algebraic theories. However, if A is infinite-dimensional, then the situation
is totally different. L. A. Kurdachenko proposed new approaches to the
study of infinite-dimensional linear groups, based on the introduced by
him a promising concept of the central dimension, and on the study of the
influence of natural families of the G-invariant subspaces on the structure
of such linear groups. Based on these investigations, a quite impressive
cycle of articles on infinite-dimensional linear groups have been written
by L. A. Kurdachenko in collaboration with M. Evans, M. R. Dixon,
I. Ya. Subbotin, J. Otal, J. M. Muños-Escolano, and N.N. Semko. The
main results of that study are published in the book Linear Groups:
“adm-n1” — 2020/5/14 — 19:35 — page — #7
Dedicated to the 70th birthday G
The Accent on Infinite Demensionality, CRC/Francis and Taylor, 2020,
written by L. A. Kurdachenko in collaboration with M. R. Dixon and
I. Ya. Subbotin.
In recent years, an important place in the research of L. A. Kur-
dachenko was occupied with issues related to important numerical invari-
ants of groups— its sectional rank, 0-rank and special rank, as well as
topics that study the relationships between factor-groups by hypercenters
and (locally) nilpotent residuals. These studies are reflected in the book
M. R. Dixon, L. A. Kurdachenko, I. Ya. Subbotin Ranks Of Groups: The
Tools, Characteristics and Restrictions, John Wiley & Sons, New Jersey,
2016.
In the last couple of years, L. A. Kurdachenko began research in
a completely new field for himself – Leibniz algebras. This is a class of non-
associative algebras that are generalizations of Lie algebras. More precisely,
Lie algebras are anti-commutative Leibniz algebras. The main emphasis
in these studies is on topics that show the specifics of Leibniz algebras,
their difference from Lie algebras, which turned out to be very significant
when considering the initial natural problems of Leibniz algebras.
One of the recent interests of L. A. Kurdachenko is in the area of fuzzy
groups. He was able to reduce the notion of a fuzzy group to an algebraic
structure which could be investigated by regular algebraic methods. It
brought a desirable order in the area of researches on fuzzy groups.
Of course, all of that is a very short and general description of L. A. Kur-
dachenko’s research achievements, and we were not able to mention many
of his important results in this brief note.
Leonid Kurdachenko is known as a great teacher. He published a couple
of text books on algebra, including the books M. R. Dixon, L. A. Kur-
dachenko, I. Ya. Subbotin An Introduction to Essential Algebraic Struc-
tures, John Wiley & Sons, Hoboken, New Jersey, 2014, and M. R. Dixon,
L. A. Kurdachenko, I. Ya. Subbotin Algebra and Number Theory: an Inte-
grated Approach, John Wiley & Sons, Hoboken, New Jersey, 2010. These
books are actively used by American and Chinese instructors in their
algebra courses. The most recent book M. R. Dixon, L. A. Kurdachenko,
“adm-n1” — 2020/5/14 — 19:35 — page H — #8
H Leonid A. Kurdachenko
I. Ya. Subbotin Ranks of Groups: The Tools, Characteristics, and Restric-
tions, John Wiley & Sons, Hoboken, New Jersey, 2017 was also used in
some lecture courses for graduate students in USA and Italy.
Leonid has many friends and collaborators around the globe. He is
a very friendly, honest, and generous person, beloved husband, father and
grandfather.
L. A. Kurdachenko is a very energetic and enthusiastic mathematician
with more achievements to come. His research activity grows every year
covering new and new areas of algebra. We warmly congratulate him on
his 70th birthday and wish him strong health and many more successful
years of research and teaching.
O. D. Artemovych, A. Ballester-Bolinches,
V. A. Bovdi, M. R. Dixon, F. de Giovanni,
R. I. Grigorchuk, W. Holubowski,
F. M. Lyman, P. Longobardi, M. Maj,
V. S. Monahov, A. S. Oliynyk, B. V. Oliynyk,
J. Otal, M. A. Perestyuk, A. P. Petravchuk,
M. V. Pratsiovytyi, A. A. Pypka, A. Russo,
A. M. Samoilenko, N. N. Semko, A. N. Skiba,
I. Ya. Subbotin, G. Vincenzi, R. A. Zatorsky,
E. I. Zelmanov, A. V. Zhuchok, Yu. V. Zhuchok
Leonid A. Kurdachenko (dedicated to 70th Birthday)
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