Hi, 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!