Algebra 04: infinite groups, linear groups

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 include the classical groups, algebraic groups, topological methods, conjugacy theorems, and finite linear groups. This book will be very useful to all mathematicians, physicists and other scientists including graduate students who use group theory in their work. Group theory is one of the most fundamental branches of mathematics. This highly accessible volume of the Encyclopaedia is devoted to two important subjects within this theory. Extremely useful to all mathematicians, physicists and other scientists, including graduate students who use group theory in their work. This volume of research papers is devoted to the field of group theory. The contributors discuss the theories of both infinite and linear groups. The contents of the text should be accessible to readers familiar with the basic concepts of algebra. It is aimed at the non-specialist A.i. Kostrikin, I.r. Shafarevich (eds.). Originally Published As V. 37 Of The Serial: Itogi Nauki I Tekhniki. Serii︠a︡ Sovremennye Problemy Matematiki. Fudamentalʹnye Napravlenii︠a︡. Includes Bibliographical References And Indexes.