# 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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