@article{4697fe71e9cd4a1a95a9c75dea426ac5,

title = "Projective pairs of profinite groups",

abstract = "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.",

keywords = "Embedding problem, PAC, Profinite group, Projective group, Pseudo algebraically closed",

author = "Lior Bary-Soroker",

note = "Funding Information: ✩ This work is a part of the author{\textquoteright}s PhD thesis done at Tel Aviv University under the supervision of Prof. Dan Haran. This research was partially supported by The Israel Science Foundation (grant No. 343/07). E-mail address: barylior@math.huji.ac.il.",

year = "2010",

month = nov,

doi = "10.1016/j.jalgebra.2010.08.011",

language = "אנגלית",

volume = "324",

pages = "2112--2128",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "9",

}