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Math Help - subset

  1. #1
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    subset

    may i know what is the different between the subgroup <H> of G and the subset H of G.

    i dont really get what it means for
    the subgroup <H> conincides with the intersection of all subgroups of G which contain the subset H
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  2. #2
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    H is a subset of G if every element of H is an element of G.

    H is a subgroup of G if H is a subset of G and H is a group.

    The subgroup generated by H is the smallest subgroup of G containing H. Informally, you need to throw as little "stuff" as possible into H until you get a group. More formally, take the intersection of all subgroups of G containing H. Since arbitrary intersections of a group form a group, you get the smallest subgroup of G that contains H.
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