STEINITZ CLASSES OF METACYCLIC EXTENSIONS

Abstract

Let $G$ be a metacyclic group of order $pq$ , where $p$ and $q$ are distinct odd prime numbers, let $N| k$ be a Galois extension whose Galois group $G(N| k)$ is isomorphic to $G$ . Let $R_N, R_k$ be the rings of integers of $N$ and $k$ . As $R_k$ -module $R_N$ is completely determined by $[N:k]$ and by its class in the class group of $R_k$ . The paper determines the classes realized by tame Galois extensions $N|k$ with $G(N|k)\cong G$ and proves that they form a group.