Recent content by Monkeyfry180

Gracias

Sounds great thank you

Huzzah.

Alright, I just did the proofs and got the same answer, thank you so much. Also, using those same values, if f1: G1 --> G is defined by f1(g) = (g, e2), how can we prove that f1 is an homomorphism, one to one, and onto?

It's easy to talk myself through associativity, but the other three are giving me trouble

Well let's say we have the two groups G1 and G2 with operations *1 and *2, respectively, and we do the cartesian product to get G1 x G2 = { (a,b) : a is an element of G1, and b is an element of G2} = G with the binary operation, * let's say, defined by (a,b) * (c,d) = (a *1 c, b *2 d)...

How do we know that the cartesian product of any two groups is also a group using the axioms of group theory?