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While searching for some useful results in Galois theory, I encountered a paper of Shafarevich from 1956 . Its first page is here:

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? )

Thanks in advance

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What paper did Shafarevich publish in 1956? There's no paper from that year on MathSciNet, except for a translation into German of a paper from 1954. Have you considered looking in Shafarevich's Collected Papers, which are translations of his work into English? – KConrad Jun 7 '13 at 15:10
up vote 4 down vote accepted

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 $G$.

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@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
Thanks a lot! If I'll have any further questions about translating from russian, I'll ask you :) – TheForumLord Jun 7 '13 at 15:41

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