Word
abelian
Phoneticsabelian
Definition
adj. 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.
adj. 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.”
Examples
simple
“The set of integers forms an abelian group under addition.”
contextual
“In an abelian group, every pair of elements commutes, meaning that the group operation is symmetric.”
complex
“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.”
Etymology
From Abel + -ian.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.