On totally real Hilbert-Speiser Fields of type C_p
Number Theory
2015-05-13 v3
Abstract
Let G be a finite abelian group. A number field K is called a Hilbert-Speiser field of type G if for every tame G-Galois extension L/K has a normal integral basis, i.e., the ring of integers O_L is free as an O_K[G]-module. Let C_p denote the cyclic group of prime order p. We show that if p >= 7 (or p=5 and extra conditions are met) and K is totally real with K/Q ramified at p, then K is not Hilbert-Speiser of type C_p.
Cite
@article{arxiv.0806.0258,
title = {On totally real Hilbert-Speiser Fields of type C_p},
author = {Cornelius Greither and Henri Johnston},
journal= {arXiv preprint arXiv:0806.0258},
year = {2015}
}
Comments
8 pages, latex, minor revisions following referee's report