I have come across the following reference to D K Faddeev's construction of quaternionic fields in the book *The Embedding Problem in Galois Theory* by Ishkhanov, Lur'e and Faddeev :


[45] D. K. Faddeev, *Construction of algebraic domains whose Galois group is the quaternionic group*, Leningrad. Gos. Univ. Uchen. Zap. **3** (1937), no. 17, 17--23,


which is presumably the same as an item in the bibliography of Faddeev's survey article [ТЕОРИЯ ГАЛУА (В МИАНе)](http://www.mathnet.ru/links/310482f639d014dafb2378061acb9088/tm2222.pdf) :


[16] *Фаддеев Д. К.* Построение алгебраических областей, группой Галуа которых является 
группа кватернионов. — Учен. зап. ЛГУ, 1936, т. 17, с. 17—25. 


**Edit** KConrad has kindly provided a link to the English translation of this survey (Спасибо, Кит). Faddeev says 



> 
> In a paper of mine in 1937 [16], the
>  problem of constructing fields with
>  quaternionic groups over $\mathbf{Q}$
>  was solved. The algebraic part of the
>  construction can be extended to any
>  field of characteristic different from
>  $2$ which has a sufficient number of
>  quadratic extensions. The arithmetic
>  part allows one to give an algorithm
>  for construction of fields over
>  $\mathbf{Q}$ in the order of growth of
>  their discriminants.
> 
> 
> 


I couldn't find this paper at [mathnet.ru](http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=21745), nor is it listed in the *Zentralblatt*. There is a later paper with a similar title


*Construction of fields of algebraic numbers whose Galois group is a group of quaternion units*, C. R. (Dokl.) Acad. Sci. URSS, n. Ser. 47, 390-392 (1945) 


which is listed but not reviewed in the *Zentralblatt*; it is not be found at [mathnet.ru](http://www.mathnet.ru/php/person.phtml?option_lang=eng&personid=21745) either.


**Question.** What does Faddeev prove in these papers ?



D K Faddeev's construction of quaternionic fields
I don't have the paper you refer to, but on the page <http://www.math.spbu.ru/vestnik/2008/vestnik0801/dfaddeev.pdf>, which is dedicated to the 100th birthday of Faddeev, his early work is described in the following way (3rd paragraph of the second page):


"The second direction which interested Faddeev in the first years of his scientific activity was Galois theory. He was especially interested in the so-called inverse Galois problem (which to this day is still not solved): construct an extension of a given base field with a prescribed Galois group. The first results of Faddeev in this area were related to the construction of extensions with small Galois groups: subgroups of $S\_4$, metacyclic transitive groups of prime degree, and groups of quaternions and quaternionic units. He used a beautiful geometric approach: the sought-after field was interpreted as a subset of a vector space on which the Galois group acts in a rather simple way. Many of the results had an elegant geometric formulation. For instance, an extension of the rationals with quaternionic Galois group is closely related to triples of pairwise orthogonal vectors in ${\mathbf R}^3$ with rational coordinates."


The article then goes on to discuss later work. 


