# Abelian Group

< MathGloss‎ | A

This glossary is far from complete. We are constantly adding math terms.
For instructions on adding new terms, please refer to Math Glossary Main Page


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)