# Difficulty understanding Russian- Paper in Galois Theory

While searching for some useful results in Galois theory, I encountered a paper of Shafarevich from 1956 . Its first page is here: http://i44.tinypic.com/2emfomw.jpg http://i44.tinypic.com/21jsrrs.jpg

and I'm mainly interested in understanding the meaning of the last formula, but the problem is that I don't understand russian (and google translate doesn't help me at all)

Can someone please explain to me what does the last formula represent? What is the meaning of each of the parameters there? ( Google translate helped me understand that $d$= rank of a group $G$ ,but can you help me understand what about the rest? )

So $n_0$ is the degree of your base field $k$ over $\mathbb{Q}_p$. The number $p^n$ is the order of your $p$-group $G$, $\alpha$ is the number of it's automorphisms. The formula gives the number of extensions of $k$ with Galois group isomorphic to $G$.
@Sasha: $\alpha$ is $|AutG|$ ? Thanks! – TheForumLord Jun 7 '13 at 14:54
@TheForumLord: Yes, that's right. $\alpha$ is the number of automorphisms of $G$. – Sasha Patotski Jun 7 '13 at 15:16