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.
@article{bwmeta1.element.bwnjournal-article-cmv81i1p153bwm,
author = {James Carter},
title = {A generalization of a result on integers in metacyclic extensions},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {153-156},
zbl = {0948.11040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv81i1p153bwm}
}
Carter, James. A generalization of a result on integers in metacyclic extensions. Colloquium Mathematicae, Tome 79 (1999) pp. 153-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i1p153bwm/
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