A generalization of a result on integers in metacyclic extensions

Tom 81 / 1999

James Carter Colloquium Mathematicum 81 (1999), 153-156 DOI: 10.4064/cm-81-1-153-156


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.


  • James Carter

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