Some results related to Hilbert's theorem 94

@article{Kisilevsky1970SomeRR,
  title={Some results related to Hilbert's theorem 94},
  author={Hershy Kisilevsky},
  journal={Journal of Number Theory},
  year={1970},
  volume={2},
  pages={199-206}
}
  • H. Kisilevsky
  • Published 1 May 1970
  • Mathematics
  • Journal of Number Theory

Relative genus theory and the class group of $l$-extensions

The structure of the relative genus field is used to study the class group of relative i-extensions. Application to class field towers of cyclic i-extensions of the rationals are given. Given a

Ostrowski quotients for finite extensions of number fields

. For L/K a finite Galois extension of number fields, the relative P´olya group Po( L/K ) coincides with the group of strongly ambiguous ideal classes in L/K . In this paper, using a well known exact

ON THE CONSTRUCTION OF RELATIVE GENUS FIELDS1

We show how to construct the relative genus field in many cases. This is then applied to constructing fields with interesting class groups. Introduction. One way to get information about the Hilbert

Capitulation, ambiguous classes and the cohomology of the units

Abstract This paper presents results on both the kernel and cokernel of the S-capitulation map for arbitrary finite Galois extensions K/F of global fields (with Galois group G) and arbitrary finite

Principalization algorithm via class group structure

For an algebraic number field K with 3-class group \(Cl_3(K)\) of type (3,3), the structure of the 3-class groups \(Cl_3(N_i)\) of the four unramified cyclic cubic extension fields \(N_i\), \(1\le

Transfers of metabelian p-groups

Explicit expressions for the transfers Vi from a metabelian p-group G of coclass cc(G) = 1 to its maximal normal subgroups M1, . . . , Mp+1 are derived by means of relations for generators. The

References

SHOWING 1-3 OF 3 REFERENCES

A remark concerning Hilbert's Theorem 94.

This paper concerns algebraic number fields k with absolute /?-class group) of type (/?, p) where p is an odd prime. p _ l Such a field has — junramified cyclic extension fields Ki of degree p. From