Projective pairs of profinite groups
| dc.creator | Bary-Soroker, Lior | |
| dc.date | 2008-10-30 | |
| dc.date.accessioned | 2026-07-07T10:14:10Z | |
| dc.date.available | 2026-07-07T10:14:10Z | |
| dc.description | We generalize the notion of a projective profinite group to a projective pair of a profinite group and a closed subgroup. We establish the 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. | |
| dc.identifier | https://arxiv.org/abs/0810.5440 | |
| dc.identifier | http://arxiv.org/abs/0810.5440 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172785 | |
| dc.subject | Group Theory | |
| dc.subject | 20E18, 12E30 | |
| dc.title | Projective pairs of profinite groups | |
| dc.type | text |