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I have a question from "A first course in abstract algebra" by J. Rotman,

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

define d(G) = dim(G/pG)

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!

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# P primary group and the correspondence theorem

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