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Why do the conjugate classes of a group partition the group?

  1. Jan 21, 2015 #1
    Given an element a in a group G,
    class(a) = {all x in G such that there exists a g in G such that gxg^(-1) = a}

    class(b) = {all x in G such that there exists a g in G such that gxg^(-1) = b}

    so let's say y is a conjugate of both a and b, so it is in both class(a) and class(b), does that mean that class(a) = class(b)?

    given there is an element y that is in both class(a) and class(b), couldn't there be an element q that is in one class and not the other?
     
  2. jcsd
  3. Jan 21, 2015 #2
    I answered my own question, can't figure out how to delete this
     
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