Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# P primary group and the correspondence theorem

**Physics Forums | Science Articles, Homework Help, Discussion**