Abelian group vs commutative group

Abelian group and commutative group both are nouns.

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

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

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

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