On embedding problems with restricted ramifications
Copyright policy )On embedding problems with restricted ramifications
Let \(L/k\) be a finite Galois extension of algebraic number fields, with Galois group \(G\), and let \( 1\to A\to E\to G\to 1\) be a central extension of groups. The author investigates the existence of the Galois extension \(M/L/k\) such that the Galois group \(\mathrm{Gal}(M/k)\) is isomorphic to \(E\) and that \(M/L\) is unramified outside a finite set of primes of \(L\). The class number of the Hilbert \(p\)-class field is also discussed.
- Kanazawa University Japan
Equations in general fields, central extension of groups, unramified extension, Galois theory, Class numbers, class groups, discriminants, algebraic number fields, Class field theory, Galois extension, class numbers
Equations in general fields, central extension of groups, unramified extension, Galois theory, Class numbers, class groups, discriminants, algebraic number fields, Class field theory, Galois extension, class numbers
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