Book III

Main algebraic structures

[141/37%]

A. I. Kostrikin

Chapter III.1Group-theoretic constructions[30/37%]

Section III.1.1Classical groups of low dimensions[5/40%]

Section III.1.2Cosets of a subgroup[2/50%]

Section III.1.3Group actions on sets[9/56%]

Section III.1.4Factor groups and homomorphisms[14/21%]

Chapter III.2Group structure[21/29%]

Section III.2.1Solvable and simple groups[4/0%]

Section III.2.2Sylow's theorems[6/50%]

Section III.2.3Finitely generated abelian groups[9/11%]

Section III.2.4Linear Lie groups[2/100%]

Chapter III.3Elements of representation theory[41/37%]

Section III.3.1Definitions and examples of linear representations[5/20%]

Section III.3.2Unitarity and reducibility[3/33%]

Section III.3.3Finite rotation groups[8/50%]

Section III.3.4Characters of linear representations[7/71%]

Section III.3.5Irreducible representations of finite groups[10/20%]

Section III.3.6Representations of the groups

\operatorname{SU}(2)

\operatorname{SO}(3)

[4/50%]

Section III.3.7Tensor product of representations[4/0%]

Chapter III.4Rings and modules[23/26%]

Section III.4.1Ring-theoretic constructions[3/33%]

Section III.4.2Individual results about rings[9/22%]

Section III.4.3Modules.[3/0%]

Section III.4.4Algebras over a field[6/50%]

Section III.4.5Irreducible modules over a Lie algebra 51(2)[2/0%]

Chapter III.5Beginning of Galois theory[26/54%]

Section III.5.1Finite field extensions[5/40%]

Section III.5.2Finite fields[9/44%]

Section III.5.3Galois correspondence[2/100%]

Section III.5.4Computing the Galois group[2/50%]

Section III.5.5Galois extensions and related issues[4/50%]

Section III.5.6Rigidity and rationality in finite groups[4/75%]

Section III.5.7Epilogue