The frattini subgroup of the absolute Galois group of a local field |
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| Authors: | Moshe Jarden Jürgen Ritter |
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| Affiliation: | 1. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel
2. Institut für Mathematik, Universit?t Augsburg, D-8900, Augsburg, West Germany
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| Abstract: | LetK be a local field,T the maximal tamely ramified extension ofK, F the fixed field inK sof the Frattini subgroup ofG(K), andJ the compositum of all minimal Galois extensions ofK containingT. The main result of the paper is thatF=J. IfK is a global field andK solv is the maximal prosolvable extension ofK, then the Frattini group of  % MathType!End!2!1!(K solv/K) is trivial. Partially supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development. |
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