# Groups (Handwritten notes)

Name | Groups (Handwritten notes)- Lecture Notes |
---|---|

Author(s) | Atiq ur Rehman |

Pages | 82 pages |

Format | PDF and DjVu (see Software section for PDF or DjVu Reader |

Size | PDF: 4.48MB, DjVu: 3.56MB |

### 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

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