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msc:notes:group-theory-important-definitions-and-results [2022/08/10 15:08] – [Download or View online] Dr. Atiq ur Rehman | msc:notes:group-theory-important-definitions-and-results [2022/08/10 15:55] (current) – removed Dr. Atiq ur Rehman | ||
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- | ====== Group Theory: Important Definitions and Results ====== | ||
- | These notes are made and shared by Mr. [[: | ||
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- | ^ Name |Group Theory: Important Definitions and Results | ||
- | ^ Author | ||
- | ^ Pages |27 pages | | ||
- | ^ Format | ||
- | ^ Size |2.21 MB | | ||
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- | ====Contents & Summary==== | ||
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- | * 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 of other subjects==== | ||
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