Abelian Group

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Abelian Group

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

[math]a, b \text { in } G \text{, } a\cdot b = b \cdot a[/math] ,

where "[math]\cdot[/math]" represents the binary operation of [math]G\,[/math].


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)