A generalization of a result on integers in metacyclic extensions

• Autorzy: James E. Carter
• Języki publikacji: EN

Abstrakty

EN

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 {\got O}_L in L as a module over ℴ.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 81
• Numer: 1
• Strony: 153-156

Daty

wydano

1999

otrzymano

1999-02-11

Twórcy

autor

James E. Carter

• Department of Mathematics, College of Charleston 66, George Street, Charleston, SC 29424-0001, U.S.A.

Bibliografia

• [1] J. E. Carter, Module structure of integers in metacyclic extensions, Colloq. Math. 76 (1998), 191-199.
• [2] A. Fröhlich and M. J. Taylor, Algebraic Number Theory, Cambridge Univ. Press, 1991.
• [3] L. R. McCulloh, Cyclic extensions without relative integral bases, Proc. Amer. Math. Soc. 17 (1966), 1191-1194.