Theory of Groups, Volume 1 by A. G. Kurosh (PDF)

Description

Translated from the second Russian edition and with added notes by K. A. Hirsch. Teoriya Grupp by Kurosh was widely acclaimed, in its first edition, as the first modern text on the general theory of groups, with the major emphasis on infinite groups. The decade that followed brought about a remarkable growth and maturity in the theory of groups, so that this second edition, an English translation, represents a complete rewriting of the first edition. The book can be used as a beginning text, the only requirement being some mathematical maturity and a knowledge of the elements of transfinite numbers. Many new sections were added to this second edition, and many old ones were completely revised: The theory of abelian groups was significantly revised; many significant additions were made to the section on the theory of free groups and free products; an entire chapter is devoted to group extensions; and the deep changes in the theory of solvable and nilpotent groups–one of the large and rich branches of the theory of groups–are covered in this work. Each volume concludes with Editor’s Notes and a Bibliography.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐good

⭐Group theory has advanced greatly since Kurosh wrote this book in 1952, and for a first course in the subject it would be inappropriate to use Kurosh as a text. However, Chelsea keeps it sporadically in print, because it’s an important book: the first book on theory of groups with a modern outlook on the subject.Kurosh was a remarkably clear thinker and writer, and K. A. Hirsch did an excellent job of translation, so this book is very readable for anyone who is already familiar with the rudiments of the subject. It’s worth careful study; not many mathematics texts give so much insight into the thinking of a master of the topic. And, algebra in general as well as group theory in particular, is more about insight than about particular results, so reading this book can help a current student of mathematics to grow in professional skill. I recommend it wholeheartedly.

⭐自分が始めて読んだ群論の洋書で、愛着の深い者なので有り難いです。

⭐

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