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He is best known for his book The Theory of Groups which was written in two volumes. He completed writing the book in 1940 but the events of World War II prevented publication of the book until 1944. In 1952 Kurosh brought out a second edition of the book which was almost a new book given as it attempted to cover the large amount of progress during the years 1940-52. The book, in the words of Kurt Hirsch who translated the book into English in 1955
has been widely acclaimed as the first modern text on the general theory of groups, with major emphasis on infinite groups.
The book includes the results for which Kurosh is best remembered, namely the Kurosh Subgroup Theorem, which describes subgroups of a free product of groups.
Among his other works Lectures on General Algebra (1960) was also translated into English by Hirsch.
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