I have searched extensively online and for copies of printed journals containing the paper which details Sanov's solution to the Burnside Problem for exponent 4, which is widely cited in many papers and texts on the Burnside problem.


The reference for the paper is I. N. Sanov, "Solution of the Burnside problem for exponent 4", *Uchen. Zap. Leningrad State Univ. Ser. Mat.* **10** (1940), 166-170 (i.e. Leningrad State University Annals).


Could anyone please help with obtaining a pdf of this, preferably in English? Thank you



Paper by I. N. Sanov, Solution of the Burnside problem for exponent 4
As it was pointed out by Alex Dugas, one can find Sanov theorem in Hall's book [here](http://books.google.com.pe/books?id=oyxnWF9ssI8C&lpg=PA429&pg=PA324#v=onepage&q&f=false), see Theorem 18.3.1. According to the author, the proof does not determine precisely the order of $B(n,4)$. However, it is quite easy to show that $B(2,4)$ is finite: $|B(2,4)|=4096$.


Let me add that the following [GAP](http://www.gap-system.org) code verifies that $|B(2,4)|\leq4096$. (Then it is easy to conclude that indeed one has $|B(2,4)|=4096$.) The idea is to generate a random set $w\_1,w\_2,\dots,w\_N$ for some big $N$ and checks whether the group $F\_2/\langle w\_1^4,...,w\_N^4\rangle$ is finite:



```
gap> f := FreeGroup(2);;
gap> a := f.1;;
gap> b := f.2;;
gap> rels := Set(List([1..10000],x->Random(f)^4));;
gap> gr := f/rels;;
gap> Order(gr);
4096

```

