## Algebra IV: Infinite Groups. Linear GroupsA.I. Kostrikin, I.R. Shafarevich 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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abelian group addition algebraic groups arbitrary automorphism basis called central Chapter characteristic classical closed commutative compact complete condition conjugacy conjugate connected consider consisting constructed contains cyclic defined Definition denote described determined dimension direct divisible elements embedded equation equivalent example exists exponent extension fact factors field finite groups free group fundamental Geometry given gives GLn(P group G group theory homomorphism identity important induction infinite invariant irreducible isomorphic known length Let G Lie groups linear groups locally matrices maximal means method module multiplication natural nilpotent normal subgroup obtained particular periodic polynomial positive presentation prime problem proof properties proved question rank reducible relations representation residually result ring satisfies shows similar soluble groups solution space structure subgroup H subset Theorem theory tion topology torsionfree unique valuation