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Junior Member

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Posted - 10/16/2007 :  05:07:52  Show Profile
If G, G are two groups and G = G G = {(a,b) such that a G, b G}, where we define (a,b)(c,d) = (ac, bd), show that:

(a) Show that N = {(a, e) such that a G}, where e is the unit element of G, is a normal subgroup of G..... I have already done this.

(b) Show that N is isomorphic to G.

(c) Show that G/N is isomorphic to G.

I did (a) but help with (b) and (c) would be great!
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