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lorena82186
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Homework Statement
If G1, G2 are two groups and G = G1 times G2 = {(a,b) such that a is an element of G1, b is and element of G2}, where we define (a,b)(c,d) = (ac, bd),
(a) Show that N = {(a, e2) such that a is an element of G1}, where e2 is the unit element of G2, is a normal subgroup of G.
(b) Show that N is isomorphic to G1.
(c) Show that G/N is isomorphic to G2.
Homework Equations
The Attempt at a Solution
I did part (a) but I do not know how to begin parts (b) and (c)