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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