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Math Help - Lagrange's Theorem and consequences

  1. #1
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    Lagrange's Theorem and consequences

    Lagrange's Theorem: |H| divides |G|.
    If G is a finite group and H is a subgroup of G, then |H| divides |G|. Moreover, the number of distinct left (right) cosets of H in G is |G|/|H|.

    I need the proof of the first Corollary: |a| divides |G|.
    In a finite group, the order of each element of the group divides the order of the group.



    Thank you!!
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  2. #2
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    Quote Originally Posted by meow91006 View Post
    Lagrange's Theorem: |H| divides |G|.
    If G is a finite group and H is a subgroup of G, then |H| divides |G|. Moreover, the number of distinct left (right) cosets of H in G is |G|/|H|.

    I need the proof of the first Corollary: |a| divides |G|.
    In a finite group, the order of each element of the group divides the order of the group.

    Thank you!!

    |a| is just the number of elements in the cyclic subgroup <a>:=\{1,a,a^2,...\}

    Tonio
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