# Group Theory by Mr. Muhammad Iftikhar

These notes are send by Mr. Muhammad Iftikhar. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org.

Name | Lecture Notes on Group Theory |
---|---|

Author | Mr. Muhammad Iftikhar |

Pages | 70 pages |

Format | PDF (see Software section for PDF Reader) |

Size | 1.8 mB |

### Contents & Summary

- Binary Operation
- Groups
- Order of a group
- Order of an element
- Periodic group
- Finite and infinite group
- Cayley table
- Klien's four group
- Involution
- Cyclic group
- Cosets
- Equivalence relation
- Lagrange's theorem
- Relation between groups
- Homomorphism
- Cayley's theorem
- Conjugacy relation in groups
- Conjugacy class
- Self conjugate
- Double cosets
- Normal subgroups and factor groups
- Factor group or quotient group
- The isomorphism theorem
- First isomorphism theorem
- Second isomorphism theorem
- Third isomorphism theorem
- Automorphism
- Inner and outer automorphism
- Complete group
- Conjugation as an automorphism
- Commutator
- Direct product

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