Algebra IV: Infinite Groups. Linear Groups

Front Cover
A.I. Kostrikin, I.R. Shafarevich
Springer Science & Business Media, Dec 22, 1993 - Mathematics - 206 pages
Group theory is one of the most fundamental branches of mathematics. This volume of the Encyclopaedia is devoted to two important subjects within group theory. The first part of the book is concerned with infinite groups. The authors deal with combinatorial group theory, free constructions through group actions on trees, algorithmic problems, periodic groups and the Burnside problem, and the structure theory for Abelian, soluble and nilpotent groups. They have included the very latest developments; however, the material is accessible to readers familiar with the basic concepts of algebra. The second part treats the theory of linear groups. It is a genuinely encyclopaedic survey written for non-specialists. The topics covered includethe classical groups, algebraic groups, topological methods, conjugacy theorems, and finite linear groups. This book will be very useful to allmathematicians, physicists and other scientists including graduate students who use group theory in their work.

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About the author (1993)

Igor Rostislavovich Shafarevich was born in Zhitomir, Ukraine on June 3, 1923. He graduated from Moscow State University with a specialty in astronomy. He taught at Moscow State University for more than 30 years. He was an internationally renowned mathematician who played a central role in the anti-Soviet dissident movement during the Cold War. His textbooks on algebraic geometry were translated into English and regarded as classics in the field. He also wrote The Socialist Phenomenon and contributed essays to From Under the Rubble. He died on February 19, 2017 at the age of 93.

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