I'm searching for a proof of Witt's result that a biquadratic extension $K(\sqrt{a},\sqrt{b})/K$ extends to a Galois extension $L/K$ with quaternion group $Q\_8$ iff the quadratic forms $<a,b,\frac{1}{ab}>, <1,1,1>$ are equivalent iff $(a,b)(a,a)(b,b) = 0 \in Br(K)$.


I know there is a proof in his original paper "Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf". However, I am searching for a proof in English. I would also like to find proofs from a more modern perspective as well as generalizations of the result.


Thank you.



Proof of Witt's result about quaternion extensions
A complete proof can be found in the first few pages of


<https://mathscinet.ams.org/mathscinet-getitem?mr=977759>


Jensen, Christian U.(DK-CPNH); Yui, Noriko(3-TRNT)
Quaternion extensions. Algebraic geometry and commutative algebra, Vol. I, 155–182, Kinokuniya, Tokyo, 1988. 


I will scan the relevant pages and post them here as soon as electricity is restored in my office.


Addendum: Here is the paper :


<https://drive.google.com/open?id=0B8EHtI8F9qdIODNpZTQ1c1JjQTlIUUdsWm1nZmxRWVNTM1Bj>


