Some properties of the absolute Galois group of a Hilbertian field (Q1088731)

The author proves the following results on the structure of absolute Galois groups G of Hilbertian fields: If the field is countable, then for almost all \(\sigma_ 1,...,\sigma_ e\) in \(G^ e\) (with respect to Haar measure) the group \(<\sigma >\) generated by \(\sigma_ 1,...,\sigma_ e\) is its own normalizer in G with trivial centralizer in case \(e>1.\) Suppose \(\tau_ 1,...,\tau_ f\) are given in \(G^ f\), then for almost all \(\sigma_ 1,...,\sigma_ e\) in the sense above \(<\tau >\cap <\sigma >=1\) holds.