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Abelian Group

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Definition

Abelian Group

A group G\, is said to be abelian if for any two elements say,

a, b \text { in } G \text{, } a\cdot b = b \cdot a ,

where "\cdot" represents the binary operation of G\,.



Examples

Examples of Abelian groups include:

  • The real numbers (under addition),
  • the non-zero real numbers (under multiplication), and
  • all cyclic groups, such as the integers (under addition)




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