Steinitz classes in generalized quaternion extensions
by
James Carter
Department of Mathematics, College of Charleston, 66 George St., Charleston, SC, 29424-0001, USA
Coauthors: Bouchaib Sodaigui

Suppose p is an odd prime and H_4p^r is the generalized quaternion group of order 4p^r. Let k be an algebraic number field with class group Cl(k) of odd order h_k. We show that if p does not divide h_k or p does not ramify in k then every class in Cl(k) can be realized as the Steinitz class of the ring of integers in a tamely ramified Galois extension of k with Galois group isomorphic to H_4p^r.

Date received: April 8, 2004