Projective pairs of profinite groups

JOURNAL OF ALGEBRA

卷:324

Article

Bary-Soroker, Lior

关键词: Profinite group;    Projective group;    Pseudo algebraically closed;    PAC;    Embedding problem;   

DOI  :  10.1016/j.jalgebra.2010.08.011

来源: Elsevier

【 摘 要 】

We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup. We establish a connection with Pseudo Algebraically Closed (PAC) extensions of PAC fields: Let M be an algebraic extension of a PAC field K. Then M/K is PAC if and only if the corresponding pair of absolute Galois groups (Gal(M),Gal(K)) is projective. Moreover any projective pair can be realized as absolute Galois groups of a PAC extension of a PAC field. Using this characterization we construct new examples of PAC extensions of relatively small fields, e.g. unbounded abelian extensions of the rational numbers. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free