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Group theory, subgroup question

  1. Jun 7, 2010 #1
    Let A be a subgroup of G. If g [tex]\in[/tex] G, prove that the set {g[tex]^{-1}[/tex] ag ; a [tex]\in[/tex] A} is also a subgroup of G.

    Thanks for any help.
     
    Last edited: Jun 7, 2010
  2. jcsd
  3. Jun 7, 2010 #2

    Mark44

    Staff: Mentor

    What's the definition of a subgroup?
     
  4. Jun 7, 2010 #3
    Thanks, mark- i left that out.

    A subset A of a group (G,*) is called a subgroup if the elements of A form a group under *.

    * is the binary operation of the two groups.
     
  5. Jun 7, 2010 #4

    Office_Shredder

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    Staff Emeritus
    Science Advisor
    Gold Member

    You have two choices:
    1) Either prove that the set is a group by confirming that it satisfies all the group axioms (there are only four, so that's not too bad)

    2) Use a theorem that allows you to confirm something is a subgroup in fewer steps (I don't know if you know any)

    Just focusing on 1, can you for example prove that the identity is contained in that set?
     
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