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Math Help - p primary group and the correspondence theorem

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    p primary group and the correspondence theorem

    Hi, this is a question from " A first course in abstract algebra" by J. Rotman

    define d(G) = dim(G/pG) (not very relevant here)

    chapter 5, lemma 5.8 (P392),

    Let G be a finite p primary abelian group.
    If S<=G, then d(G/S) <= d(G)

    The first line of the proof read like,


    By the correspondence theorem, p(G/S) = (pG +S)/S,

    How is this equation derived? As the correspondence theorem mainly states isomorphism, I cannot see where there is equation involved? It would be greatly appreciated if anyone could help on this. Many thanks!
    Last edited by JZ2012; June 17th 2012 at 06:03 AM.
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