Groups (Handwritten Notes)

Groups; definition and examples

Order of group, order of element

Periodic group, mixed group

Subgroup

Invalution

Relation between groups, homomorphism, monomorphism, epimorphism, isomorphism, endomorphism, examples and related theorem

Kernel, definition and related theorems

Cyclic group, related theorems

Complex in a group, product of complexes and related theorems

Coset, definition and examples

Index of subgroup, Lagrange's theorem

Double coset, related theorem

Normalizer, definition and related theorems

Centralizer, centre of group, related theorem

Conjugate or transform of a group, definition and related theorems

Self conjugate, conjugancy class, related theorem

Class equation, p-group, definition and related theorems

Conjugate subgroup, definition and related theorems

Normal subgroup, definition and related theorems

Factor or quotient group, definition and related theorem

1st isomorphism theorem, related theorem

2nd isomorphism theorem

3rd isomorphism theorem

Endomorphism, automorphism, definition and related theorem

Conjugation as an automorphism

Inner and outer automorphism, definition and related theorems

Commutator of a group, definition and related theorem

Derive group or commutative group, definition and related theorem

Direct product of groups, definition and related theorems

Invariant subgroup

Characteristic subgroup

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