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What does this definition mean ?

  1. Oct 9, 2012 #1
    hello , I don't understand the meaning of the next definition , so , I hope that you can make it easy to understand it for me

    if G is an arbitrary group and ∅≠S⊆G , then ,the symbol (s) will represent the set
    (S) = ∩ { H∖S ⊆ H : H is a subgroup of G }

    can you give me some examples about this definition ?
  2. jcsd
  3. Oct 9, 2012 #2

    Stephen Tashi

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    Science Advisor

    Perhaps the definition should read: (S) = ∩ { H | S ⊆ H : H is a subgroup of G }
    where "H |" means "the H such that...".

    (The notation "H\G" is used by some books to denote the set of right cosets of a subgroup H. I don't think that is what the definition uses.)

    The usual definition of (S) would be called "the subgroup generated by S" and it would be
    [itex] \cap_i H_i [/itex] taken over all subgroups [itex] H_i [/itex] of [itex] G [/itex] that contain [itex] S [/itex] as a subset.

    What examples of finite groups have you studied? Perhaps we can use one of them as an example.
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