I am having trouble distinguishing some terms here. I got these from my book
A group is a nonempty set G together with binary operation * that satisfies the three properties
If a group also satisfies Commutativity, then it is abelian, if it doesn't then it is nonabelian
Okay here is my confusion, the last statement seems to throw the term group aside. Is it basically telling me to check whether Commutativity is satisfied or not and label them abelian and nonabelian?