alt Hacker NewsSo...an abelian group is both associative (because it's a group) and commutative (because it's abelian), which is exactly what the OP said? It sounds like you're disagreeing about something, but I'm not clear what your objection is.
So...an abelian group is both associative (because it's a group) and commutative (because it's abelian), which is exactly what the OP said? It sounds like you're disagreeing about something, but I'm not clear what your objection is.
I’m not disagreeing. I’m pointing out that in TFA it sounds as associativity is a property of abelian groups specifically whereas it as a property of all groups in general. In that sense it’s not wrong, just the emphasis is a bit misleading.
If you look in an abstract algebra textbook they all basically say the same definition for abelian groups (eg in Hien)
> “A group G is called abelian if its operation is commutative ie for all g, h in G, we have gh = hg”.