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Abstract
In Citation[1], the author gave a positive solution to the problem in the survey of Jarden Citation[2] on the closedness of the class of profinite groups that are isomorphic to absolute Galois groups of fields with respect to finite free products. In Citation[3], O. V. Mel'nikov solved this problem for separable profinite groups (Citation[3] was done earlier than Citation[1]). In the same case, a more exact result on the absolute Galois groups of fields of fixed characteristic was obtained there. The proof proposed in Citation4-5 is simpler than that in Citation[1] and, in addition, provides the results of Mel'nikov.
On February, 2000, the author (knowing nothing about Citation4-5) found one more proof of these results. In the author opinion, this proof is the simplest and the construction used in the proof, as well as its properties (cf. Propositio n 1) can have other applications.