Composita of symmetric extensions of Q

WD Geyer, M Jarden, A Razon

Research output: Contribution to journalArticlepeer-review


Let K be a Hilbertian presented field with elimination theory of characteristic
≠ 2, let Ksymm be the compositum of all symmetric extensions of K, and let Ksymm,ins be the maximal purely inseparable extension of Ksymm. Then, Th(Ksymm,ins) is a primitive recursive theory. Moreover, the set of finite groups that can be realized as Galois groups over K in Ksymm as well as the set of finite groups that occur as Galois groups over Ksymm are primitive recursive subsets of the set of all finite groups. Finally, if K is countable, then Gal(Ksymm/K) ∼= Gal(Qsymm/Q).
Original languageEnglish
Pages (from-to)139-161
Number of pages23
JournalMünster J. Math.
Issue number1
StatePublished - 2019


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