Groups (Handwritten notes)

CONTENTS OR SUMMARY:

• 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