Geodesic
Infinitude of the number of relations in the Galois group of the maximal $p$-extension of a local field with restricted ramification
Izvestiya. Mathematics , Tome 18 (1982) no. 3, pp. 513-524.

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This paper contains a proof of the theorem announced in RZh.Mat., 1977, A390. Bibliography: 7 titles. 
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N. L. Gordeev. Infinitude of the number of relations in the Galois group of the maximal $p$-extension of a local field with restricted ramification. Izvestiya. Mathematics , Tome 18 (1982) no. 3, pp. 513-524. http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a4/

[1] Gordeev N. L., “Beskonechnost chisla sootnoshenii v gruppe Galua maksimalnogo $p$-rasshireniya s ogranichennym vetvleniem lokalnogo polya”, Dokl. AN SSSR, 233:6 (1977), 1031–1034 | MR | Zbl

[2] Gordeev N. L., “Gruppy vetvleniya beskonechnykh $p$-rasshirenii lokalnogo polya”, Zap. nauchn. seminarov LOMI, 71, 1977, 96–132 | MR | Zbl

[3] Maus E., “On the jumps in the series of ramification groups”, Bull. Soc. Math. France, 25 (1971), 127–133 | MR | Zbl

[4] Maus E., “Relationen in Verzweigungsgruppen”, J. Reine Ang. Math., 258 (1973), 23–50 | MR | Zbl

[5] Cepp Zh.-P., Kogomologii Galua, Mir, M., 1968 | MR

[6] Serre J.-P., Corps locaux, Publications de l'Institut de Mathématique de l'Université de Nancago, VIII, Actualités Sci. Indust., No. 1296. Hermann, Paris, 1962 | MR

[7] Hasse H., Zahlentheorie, Berlin, 1963 | MR