Abstract Algebra: Proving Normal Subgroup and Isomorphisms

[lorena82186]

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)

 

[mjsd]

understand what is the definition for isomorphism (ie. need to find a 1-1 mapping from elements in N to elements in G1 such that the multiplication table is the same)

 

[matt grime]

(b) write down the only conceivable map, and show it is an isomorphism

(c) see (b).