Closed Subgroups of G(Q) with Involutions
نویسنده
چکیده
The aim of this note is to determine certain closed subgroups of the absolute Galois group G(Q) of Q, in particular subgroups generated by involutions (=elements of order 2). Geyer [3,4.1] has shown, in a far more general set-up, that subgroups generated by finitely many involutions are almost always free profinite products of copies of Z/22. To be precise, fix an involution E E G(Q); for almost all (in the sense of the Haar measure) e-tuples (cl, . . . . a,) in G(Q)e= G(Q) x .+. x G(Q) (e copies) we have
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