Zusammenfassung
The absolute Galois group of a PAC field is projective (Theorem 10.17). This chapter includes a converse (Corollary 20.16): If G is a projective group, then there exists a PAC field K such that G (K) ≅ G. Projective groups also appear as the universal Frattini covers of profinite groups (Proposition 20.33). Thus, as preparation for decidability and undecidability results about families of PAC fields, we introduce the basic properties of Frattini covers.
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Notes
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© 1986 Springer-Verlag Berlin Heidelberg
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Fried, M.D., Jarden, M. (1986). Projective Groups and Frattini Covers. In: Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07216-5_20
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DOI: https://doi.org/10.1007/978-3-662-07216-5_20
Publisher Name: Springer, Berlin, Heidelberg
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