commutative group vs Abelian group

commutative group and Abelian group both are nouns.

Word	Noun	Adjective	Verb	Adverb
commutative group	Yes	No	No	No
Abelian group	Yes	No	No	No

As nouns, commutative group and Abelian group are synonyms defined as:

commutative group and Abelian group: a group that satisfies the commutative law

commutative group (noun)	Abelian group (noun)
a group that satisfies the commutative law	a group that satisfies the commutative law