Extensions with Archimedean ramification points

V. A. Babaitsev

M. V. Lomonosov Moscow State University

Abstract: A subgroup of the Galois group of an extension of an algebraic number field that is closed with respect to 2-extensions is considered. This subgroup is generated by the inertia sub-groups of the real points of the maximal real subfield. It is proved that this group is the free product of the Cantor set of cyclic groups of order 2 in the category of pro-2-groups.

UDC: 511

Received: 04.08.1971

 English version: Mathematical Notes, 1973, 14:1, 589–592

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