Alexander Gennadyevich Kurosh (Russian: Александр Геннадиевич Курош; January 19, 1908 – May 18, 1971) was a Soviet mathematician, known for his work in abstract algebra. He is credited with writing the first modern and high-level text on group theory, his The Theory of Groups published in 1944.
He was born in Yartsevo near Smolensk, and died in Moscow. He received his doctorate from the Moscow State University in 1936 under the direction of Pavel Alexandrov. In 1938, he was the PhD thesis adviser to fellow group theory pioneer Sergei Chernikov, 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.
- He published in Spanish "Curso de Álgebra Superior"
- Gruppentheorie. 2 vols., 1953, 1956, Akademie Verlag, Berlin, 2nd edition 1970, 1972.
- Vorlesungen über Allgemeine Algebra. Verlag Harri Deutsch, Zürich 1964.
- Zur Theorie der Kategorien. Deutscher Verlag der Wissenschaften, 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 Unterprodukte 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.
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