Group Theory: Important Definitions and Results

Group Theory: Important Definitions and Results These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on These notes contains important definitions with examples and related theorem, which might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.

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
  • 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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  • notes/group-theory-important-definitions-and-results
  • Last modified: 16 months ago
  • by Dr. Atiq ur Rehman