Abstract
AbstractThe structure of Kronecker class of an extension K: k of algebraic number fields of degree |K: k| ≤ 8 is investigated. For such classes it is shown that the width and socle number are equal and are at most 2, and for those of width 2 the Galois group is given. Further, if |K: k | is 3 or 4, or if 5 ≤ |K: k| ≤ 8 and K: k is Galois, then the groups corresponding to all “second minimal” fields in K are determined.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Reference13 articles.
1. On octic field extensions and a problem in group theory
2. On Kronecker Classes of Atomic Extensions
3. Rigidity of decomposition laws and number fields;Klingen;J. Austral. Math. Soc., Ser. A
4. On a question of W. Jehne concerning covering subgroups of groups and Kronecker classes of fields;Saxl;Proc. London Math. Soc.
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