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Math Help - Homomorphism 6

  1. #1
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    Homomorphism 6

    If G is a group and N is a normal subgroup of G, show that if a in G has finite order o(a), then Na in G/N has finite order m, where m|o(a). (Prove this by using the homomorphism of G onto G/N.)
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    Quote Originally Posted by mpryal View Post
    If G is a group and N is a normal subgroup of G, show that if a in G has finite order o(a), then Na in G/N has finite order m, where m|o(a). (Prove this by using the homomorphism of G onto G/N.)
    Let \pi : G\to G/N be the natural projection homomorphism i.e. g\mapsto gN.
    Let a\in G then order of \pi (a) must divide order of a by the properties of homomorphism.
    Thus, we see that m | \text{o}(a).
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