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Introduction to algebra
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III · Main algebraic structures
Chapter III.2
Group structure
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III.2.1 · Solvable and simple groups
III.2.2 · Sylow's theorems
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III.2.3 · Finitely generated abelian groups
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III.2.4 · Linear Lie groups
Section III.2.1
Solvable and simple groups
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Subsection III.2.1.1
Solvable groups
Subsection III.2.1.2
Simple groups
Section III.2.2
Sylow's theorems
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Section III.2.3
Finitely generated abelian groups
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Subsection III.2.3.1
Examples and preliminary results
Subsection III.2.3.2
Torsion-free Abelian groups
Subsection III.2.3.3
Free abelian groups of finite rank
Subsection III.2.3.4
The structure of finitely generated abelian groups
Subsection III.2.3.5
Other approaches to the classification problem
Subsection III.2.3.6
The main theorem on finite abelian groups
Section III.2.4
Linear Lie groups
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Subsection III.2.4.1
Definitions and examples
Subsection III.2.4.2
Curves in matrix groups
Subsection III.2.4.3
The differential of a homomorphism
Subsection III.2.4.4
Lie algebra of a Lie group
Subsection III.2.4.5
Logarithm