Free products of absolute Galois groups (Q1840960)

The main goal of this paper under review is to give an affirmative answer to Problem 18 in \textit{M. Jarden}'s survey [Infinite Galois theory, Handbook of algebra. Vol. 1, 269-319 (1996; Zbl 0864.12003)]. This problem asks whether the free product of \(n\) absolute Galois groups of fields is also an absolute Galois group of a field. The author states the following theorem: Let the profinite groups \(G_1, \ldots, G_n\) be isomorphic to absolute Galois groups of fields. Then their free product \(G_1 \ast \cdots \ast G_n\) is also isomorphic to an absolute Galois group of a field of characteristic zero. Note that meanwhile a similar result concerning also the positive characteristic case is obtained by \textit{O. V. Mel'nikov} [Sib. Math. J. 40, No. 1, 95-99 (1999; Zbl 0935.12005)] using different methods.