Geodesic
Construction of cyclic extensions of degree $p^2$ for a~complete field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 52-66

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In the present paper we embed a given cyclic extension of degree $p$ of a complete discrete valuation field of characteristic 0 with an arbitrary residue field of characteristic $p>0$ into a cyclic extension of degree $p^2$. The result extends the construction obtained by S. V. Vostokov and I. B. Zhukov in terms of Witt vectors, to a wider interval of values for the ramification jump of the original field extension. 
@article{ZNSL_2017_455_a5,
     author = {I. Zhukov and E. Lysenko},
     title = {Construction of cyclic extensions of degree $p^2$ for a~complete field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--66},
     publisher = {mathdoc},
     volume = {455},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a5/}
}
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I. Zhukov; E. Lysenko. Construction of cyclic extensions of degree $p^2$ for a~complete field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 52-66. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a5/