# Abelian

CEFR C2 · Adjective

Source: https://englishreference.com/word/abelian
Updated: 2026-08-15

## Definition

describing a group where the order of the numbers or elements does not matter. In math, this means 2 + 3 is the same as 3 + 2.

For teachers: relating to a group in which the binary operation is commutative. In such a group, the order of the operands does not affect the result of the operation.

## Examples

- The set of integers forms an abelian group under addition.
- In an abelian group, every pair of elements commutes, meaning that the group operation is symmetric.
- The classification of finite abelian groups is a fundamental result in algebra, showing that every such group is a direct sum of cyclic groups of prime power order.

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