306: Group

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A definition of group

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Topics

About: group

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Definition

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Starting Context

• The reader knows a definition of set.

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Target Context

• The reader will have a definition of group.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Definition

Any set, S, with any binary operation (called 'group operation'), $\bullet :S\times S\to S$, such that for any elements, $p_1,p_2,p_3\in S$, 1) $(p_1\bullet p_2)\bullet p_3=p_1\bullet (p_2\bullet p_3)$; 2) $i\in S$ (called 'identity element') such that $i\bullet p_1=p_1\bullet i=p_1$; 3) $p_1^{-1}\in S$ (called 'inverse element of $p_1$') such that $p_1^{-1}\bullet p_1=p_1\bullet p_1^{-1}=i$

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References

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