Geodesic
On some 2-extension of the field $\mathbb Q$ of rational numbers
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 192-196 
V. M. Tsvetkov. On some 2-extension of the field $\mathbb Q$ of rational numbers. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 192-196. http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a21/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is proved that the field $\mathbb Q$ of rational numbers has one and only one normal 2-extension $\mathbb Q_{(2,\infty)}/\mathbb Q$ with the groupe isomorphic to $Z_2*\mathbb Z/2$. If $\Omega$ the maximal subfield of a real-closed field not contain in $\sqrt 2$, then the algebraic closure $\overline\Omega$ is isomorphic to the field $\Omega\underset{\mathbb Q}{\otimes}\mathbb Q_{(2,\infty)}$.

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