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Abstract Algebra | Definition of a Group and Basic Examples
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Abstract Algebra - The Basics of Groups
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- 1 Abstract Algebra | Definition of a Group and Basic Examples
- 2 Abstract Algebra | General properties of groups.
- 3 Abstract Algebra | Group of Units modulo n
- 4 Abstract Algebra | The notion of a subgroup.
- 5 Abstract Algebra | The subgroup test
- 6 Abstract Algebra | The center of a group.
- 7 Abstract Algebra | Coset equality.
- 8 Abstract Algebra | Lagrange's Theorem
- 9 Abstract Algebra | Group Isomorphisms
- 10 Abstract Algebra | Properties of isomorphisms.
- 11 Abstract Algebra | The classification of cyclic groups.
- 12 Lots of group isomorphism examples.
- 13 Abstract Algebra | Cayley's Theorem
- 14 Abstract Algebra | Direct product of groups.
- 15 Abstract Algebra | Internal direct product of subgroups.
- 16 Abstract Algebra | Group homomorphisms
- 17 Abstract Algebra | Normal Subgroups
- 18 Abstract Algebra | Quotient Groups
- 19 Abstract Algebra | Subgroups and quotient groups of the quaternions.
- 20 Abstract Algebra | If G/Z(G) is cyclic then G is abelian.
- 21 Abstract Algebra | Homomorphisms and the order of an element.
- 22 Abstract Algebra | The kernel of a homomorphism
- 23 Abstract Algebra | When is this a homomorphism?
- 24 Abstract Algebra | First Isomorphism Theorem for Groups
- 25 Abstract Algebra | The Second Isomorphism Theorem for Groups
- 26 Abstract Algebra | The inner automorphisms of a group.
- 27 Abstract Algebra | The third isomorphism theorem for groups.
- 28 Abstract Algebra | A nice application of the second isomorphism theorem.
- 29 Abstract Algebra | Third isomorphism application.
