Extensions with Archimedean ramification points

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.Translated from Matematicheskie Zametki, Vol. 14, No. 1, pp. 61–66, July, 1973.The author would like to thank L. V. Kuz'min for his guidance in this paper and E. S. Golod for his improving comments.