# Group Theory: Important Definitions and Results

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Name | Group Theory: Important Definitions and Results |
---|---|

Author | Mr. Akhtar Abbas |

Pages | 27 pages |

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

Size | 2.21 MB |

### Contents & Summary

- A non-empty set $G$ with binary operation * is called group if the binary operation * is associative and
- (1) for all $a\in G$, $\exists$ $e\in G$ s.t $a\text{*} e= e\text{*} a =$
- (2) for each $a\in G$, $\exists$ $a^{-1}\in G$ s.t $a\text{*} a^{-1}=a^{-1}\text{*} a =e$.

- In a group $G$, there is only one identity element.
- In a group $G$, the inverse of the element is unique.
- Every element of $A_n$ is a product of 3-cycles, $n\geq 3$.

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