TITLE: Group theory notation
QUESTION [8 upvotes]: What does the notation $(G,.)$ mean in group theory? I have seen in places that $.$ implies the binary operation multiplication on group $G$. But then, why do we show an abelian group as $(G, +)$? And what is additive and multiplicative notation?

REPLY [3 votes]: "But is there any particular underlying reason? – Artemisia"

I can't reply yet above, but I would think that (G,+) is used when the law of composition is commutative because (for example) matrix ADDITION is commutative, but matrix MULTIPLICATION is not, although both operations on matrices are associative.  This convention may have arisen here.  Recall that it is probably unnecessary to explain WHY conventions are the way they are in most cases....