Some remarks on Hilbert-Speiser and Leopoldt fields of given type

James E. Carter. "Some remarks on Hilbert-Speiser and Leopoldt fields of given type." Colloquium Mathematicae 108.2 (2007): 217-223. <http://eudml.org/doc/286266>.

@article{JamesE2007,
abstract = {Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers $O_\{L\}$ in L is free as a module over the associated order $_\{L/K\}$. We also give examples, some of which show that this result can still hold without the assumption that K contains a primitive pth root of unity.},
author = {James E. Carter},
journal = {Colloquium Mathematicae},
keywords = {normal integral bases; class groups; associated orders},
language = {eng},
number = {2},
pages = {217-223},
title = {Some remarks on Hilbert-Speiser and Leopoldt fields of given type},
url = {http://eudml.org/doc/286266},
volume = {108},
year = {2007},
}

TY - JOUR
AU - James E. Carter
TI - Some remarks on Hilbert-Speiser and Leopoldt fields of given type
JO - Colloquium Mathematicae
PY - 2007
VL - 108
IS - 2
SP - 217
EP - 223
AB - Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers $O_{L}$ in L is free as a module over the associated order $_{L/K}$. We also give examples, some of which show that this result can still hold without the assumption that K contains a primitive pth root of unity.
LA - eng
KW - normal integral bases; class groups; associated orders
UR - http://eudml.org/doc/286266
ER -