J Austral Math Soc Ser A 57 pp17--34, 1994.

Kronecker Classes of Fields and Covering Subgroups of Finite Groups

Cheryl E. Praeger

Abstract

Kronecker classes of algebraic number fields were introduced by W. Jehne in an attempt to understand the extent to which the structure of an extension K : k of algebraic number fields was influenced by the decomposition of primes of k over K. He found an important link between Kronecker equivalent field extensions and a certain covering property of their Galois groups. This paper surveys recent contributions of Group Theory to the understanding of Kronecker equivalence of algebraic number fields. In particular some group theoretic conjectures related to the Kronecker class of an extension of bounded degree are explored.

1991 AMS Subject Classification: 20B25, 12F10

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Authors

Cheryl E. Praeger

University of Western Australia, Nedlands, WA 6009, Australia.