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more homomorphism theorems

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lorena82186
Junior Member

USA
4 Posts

Posted - 10/17/2007 : 04:27:15

If G

, G

are two groups and 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

}, 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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