Geodesic
Constructing quaternionic fields
Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 43-54

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a field of characteristic different from 2, and a, b quadratically independent elements of K. Put J= K(√a, √b). In [4], Jensen and Yui discuss the question of quaternionic (Q8) extensions of J, and give a survey of known results. In [8], Ware discusses (among other things) some general conditions for, and relations between, the existence of Q8 and D4 (dihedral) extensions of K. A general theorem of Witt [9] says that J will have a quaternionic extension J(√u) if and only if there exists a 3 × 3 matrix P over K such that PPt = diag(a, b, 1/ab), and an appropriate value for u is given in terms of the entries of P. The problem of actually finding P in a particular case is not trivial. 
Vaughan, Theresa P. Constructing quaternionic fields. Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 43-54. doi: 10.1017/S0017089500008533
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