Aleksandr Gennadyevich Kurosh (russian: Алекса́ндр Генна́диевич Ку́рош; January 19, 1908 – May 18, 1971) was a
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, known for his work in
abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...
. He is credited with writing ''The Theory of Groups'', the first modern and high-level text on
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, published in 1944.
He was born in
Yartsevo Yartsevo (russian: Ярцево) is the name of several inhabited localities in Russia.
;Urban localities
*Yartsevo, Smolensk Oblast, a town in Yartsevsky District of Smolensk Oblast; administratively incorporated as Yartsevskoye Urban Settlement ...
, in the
Dukhovshchinsky Uyezd of the
Smolensk Governorate
Smolensk Governorate (russian: Смоленская губерния, Smolenskaja gubernija), or the Government of Smolensk, was an administrative division (a '' guberniya'') of the Tsardom of Russia, the Russian Empire, and the Russian SFSR. It ex ...
of the
Russian Empire
The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...
and died in
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 millio ...
. He received his doctorate from the
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
in 1936 under the direction of
Pavel Alexandrov
Pavel Sergeyevich Alexandrov (russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about three hundred papers, ma ...
. In 1937 he became a professor there, and from 1949 until his death he held the Chair of Higher Algebra at Moscow State University. In 1938, he was the PhD thesis adviser to his fellow group theory scholar
Sergei Chernikov
Sergei Nikolaevich Chernikov (11 May 1912 – 23 January 1987; russian: Сергей Николаевич Черников) was a Russian mathematician who contributed significantly to the development of infinite group theory and linear inequalit ...
, with whom he would develop important relationships between finite and infinite groups, discover the Kurosh-Chernikov class of groups, and publish several influential papers over the next decades. In all, he had 27 PhD students, including also
Vladimir Andrunakievich,
Mark Graev, and
Anatoly Shirshov.
Selected publications
* ''Teoriya Grupp'' (''Теория групп''), 2 vols., Nauk, 1944, 2nd edition 1953.
** German translation: ''Gruppentheorie.'' 2 vols., 1953,
1956,
Akademie Verlag
:''There also were unrelated publishing houses in Stuttgart and in (East-)Berlin, and there is the (JAVG).''
Akademie Verlag (AV) is a German scientific and academic publishing company, founded in 1946 in the Soviet-occupied eastern part ...
, Berlin, 2nd edition 1970, 1972.
** English translation: ''The Theory of Groups'', 2 vols.,
Chelsea Publishing Company The Chelsea Publishing Company was a publisher of mathematical books, based in New York City, founded in 1944 by Aaron Galuten while he was still a graduate student at Columbia
Columbia may refer to:
* Columbia (personification), the historical ...
, the
Bronx
The Bronx () is a borough of New York City, coextensive with Bronx County, in the state of New York. It is south of Westchester County; north and east of the New York City borough of Manhattan, across the Harlem River; and north of the New Y ...
, tr. by
K. A. Hirsch, 1950, 2nd edition 1955.
* ''Vorlesungen über Allgemeine Algebra.''
Verlag Harri Deutsch
The (VHD, HD) with headquarters in Frankfurt am Main, Germany, as well as in Zürich and Thun, Switzerland, was a German publishing house founded in 1961 and closed in 2013.
Overview
The ' with headquarters in Frankfurt am Main, Germany, w ...
, Zürich 1964.
* ''Zur Theorie der Kategorien.''
Deutscher Verlag der Wissenschaften
(DVW) (English: ''German Publisher of Sciences'') was a scientific publishing house in the former German Democratic Republic (GDR/).
Situated in Berlin, DVW was founded as (VEB) on 1 January 1954 as the successor of the main department of "un ...
, Berlin 1963.
* Kurosch
''Zur Zerlegung unendlicher Gruppen.''Mathematische Annalen vol. 106, 1932.
* Kurosch
''Über freie Produkte von Gruppen.''Mathematische Annalen vol. 108, 1933.
* Kurosch
''Die Untergruppen der freien Produkte von beliebigen Gruppen.''Mathematische Annalen, vol. 109, 1934.
* A. G. Kurosh, S. N. Chernikov, “Solvable and nilpotent groups”, Uspekhi Mat. Nauk, 2:3(19) (1947), 18–59.
* A. G. Kurosh, "Curso de Álgebra Superior", Editorial Mir, Moscú 1997, traducción de Emiliano Aparicio Bernardo (in Spanish)
See also
*
Kurosh subgroup theorem In the mathematical field of group theory, the Kurosh subgroup theorem describes the algebraic structure of subgroups of free products of groups. The theorem was obtained by Alexander Kurosh, a Russian mathematician, in 1934. Informally, the theor ...
*
Kurosh problem
References
External links
*
*
{{DEFAULTSORT:Kurosh, Aleksandr
1908 births
1971 deaths
20th-century Russian mathematicians
People from Yartsevo
People from Dukhovshchinsky Uyezd
Academic staff of Moscow State University
Academic staff of Saratov State University
Moscow State University alumni
Recipients of the Order of the Red Banner of Labour
Recipients of the USSR State Prize
Algebraists
Number theorists
Topologists
Russian mathematicians
Soviet mathematicians
Burials at Vvedenskoye Cemetery