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Abstract algebra

  1. Oct 16, 2007 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations

    3. The attempt at a solution
    I did part (a) but I do not know how to begin parts (b) and (c)
  2. jcsd
  3. Oct 16, 2007 #2


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    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)
  4. Oct 16, 2007 #3

    matt grime

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

    (c) see (b).
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