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Math Help - Isotropy Group and equivalent relation

  1. #1
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    Isotropy Group and equivalent relation

    Hello,

    my english is not so good, but i try my best to explain my problems to you.

    I have a problem with following situation:

    Let G be a group, A a arbitrary set, f:G x A->A a group action and G_a the isotropy group of a \in A.

    Now my professor has denoted followin equiv. relation on G:

    g ~ g'<=>ga=g'a<=>g'^(-1)g=g^(-1)g' \in G_a <=> g=g'mod G_a =>Ga~G/G_a

    And my question is, what does Ga~G/G_a means? i never had seen this before.

    I hope you can understand my problem. If not, please tell me which part you dont understand.

    Thank you.
    Last edited by Sogan; October 24th 2010 at 06:04 AM.
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  2. #2
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    It says that G_a, the isotropy group of a, is isomorphic to the quotient group G/G_a. Have you dealt with quotient groups?
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  3. #3
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    Oh yes, thank you for your help.

    Yes i know the Quotient Group. Now i'm clear in that point.

    thanks a lot.
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