Let G = (G, . , e), H = (H , * , E) be groups ... (e is the identity)
the direct product is defined by:
G x H = (GXH, o , (e,E)) where,
(g1,h1) o (g2,h2) = (g1 . g2, h1*h2)
Question: Show formally that G x H is a group.
when it says, "show formally that G x H is a group".. does it mean show that G x H satisfies the 4 conditions for being a group.. i.e.
existance of identity element and
existance of inverse element?
any help is appreciated..