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

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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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     author = {V. M. Tsvetkov},
     title = {On some 2-extension of the field~$\mathbb Q$ of rational numbers},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {192--196},
     publisher = {mathdoc},
     volume = {236},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a21/}
}
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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/