Embedding covers and the theory of frobenius fields
Copyright policy )Embedding covers and the theory of frobenius fields
We show that the theory of Frobenius fields is decidable. This is conjectured in [4], [8] and [13], and we prove it by solving a group theoretic problem to which this question is reduced there. To do this we present and develop the notion of embedding covers of finite and pro-finite groups. We also answer two other problems from [8], again by solving a corresponding group theoretic problem: A finite extension of a Frobenius field need not be Frobenius and there are PAC fields which are not Frobenius fields.
- Tel Aviv University Israel
- Bar-Ilan University Israel
Decidability and field theory, absolute Galois groups, PAC-fields, decidability, universal embedding cover, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), superprojective group, universal Frattini cover, projective profinite groups, Frobenius fields, embedding property, primitive recursive, Limits, profinite groups, pseudo-algebraically closed field
Decidability and field theory, absolute Galois groups, PAC-fields, decidability, universal embedding cover, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), superprojective group, universal Frattini cover, projective profinite groups, Frobenius fields, embedding property, primitive recursive, Limits, profinite groups, pseudo-algebraically closed field
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