A generalization of a result on integers in metacyclic extensions
Colloquium Mathematicae (1999)
- Volume: 81, Issue: 1, page 153-156
- ISSN: 0010-1354
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topCarter, James. "A generalization of a result on integers in metacyclic extensions." Colloquium Mathematicae 81.1 (1999): 153-156. <http://eudml.org/doc/210725>.
@article{Carter1999,
abstract = {Let p be an odd prime and let c be an integer such that c>1 and c divides p-1. Let G be a metacyclic group of order pc and let k be a field such that pc is prime to the characteristic of k. Assume that k contains a primitive pcth root of unity. We first characterize the normal extensions L/k with Galois group isomorphic to G when p and c satisfy a certain condition. Then we apply our characterization to the case in which k is an algebraic number field with ring of integers ℴ, and, assuming some additional conditions on such extensions, study the ring of integers OL in L as a module over ℴ.},
author = {Carter, James},
journal = {Colloquium Mathematicae},
keywords = {Steinitz classes; algebraic integers; class group; metacyclic extensions; Galois group; tamely ramified extensions},
language = {eng},
number = {1},
pages = {153-156},
title = {A generalization of a result on integers in metacyclic extensions},
url = {http://eudml.org/doc/210725},
volume = {81},
year = {1999},
}
TY - JOUR
AU - Carter, James
TI - A generalization of a result on integers in metacyclic extensions
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 1
SP - 153
EP - 156
AB - Let p be an odd prime and let c be an integer such that c>1 and c divides p-1. Let G be a metacyclic group of order pc and let k be a field such that pc is prime to the characteristic of k. Assume that k contains a primitive pcth root of unity. We first characterize the normal extensions L/k with Galois group isomorphic to G when p and c satisfy a certain condition. Then we apply our characterization to the case in which k is an algebraic number field with ring of integers ℴ, and, assuming some additional conditions on such extensions, study the ring of integers OL in L as a module over ℴ.
LA - eng
KW - Steinitz classes; algebraic integers; class group; metacyclic extensions; Galois group; tamely ramified extensions
UR - http://eudml.org/doc/210725
ER -
References
top- [1] J. E. Carter, Module structure of integers in metacyclic extensions, Colloq. Math. 76 (1998), 191-199. Zbl0995.11061
- [2] A. Fröhlich and M. J. Taylor, Algebraic Number Theory, Cambridge Univ. Press, 1991. Zbl0744.11001
- [3] L. R. McCulloh, Cyclic extensions without relative integral bases, Proc. Amer. Math. Soc. 17 (1966), 1191-1194. Zbl0144.29405
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