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The generalized Rédei-matrix for function fields. (English) Zbl 1292.11130

The classical Rédei matrix was introduced by L. Rédei [J. Reine Angew. Math. 171, 131–148 (1934; Zbl 0009.29302)] in order to study the \(4\)-rank of the ideal class groups of quadratic number fields. This article begins with a valuable survey of previous work in this area, and then the authors define the generalized Rédei matrix for cyclic extensions of prime degree \(\ell\) in the function field case and point out connections with the exact hexagon introduced by P. E. Conner and J. Hurrelbrink [Class number parity. Singapore etc.: World Scientific (1988; Zbl 0743.11061)]. Finally they apply their results to special cases, such as biquadratic extensions, Kummer extensions and Artin-Schreier extensions.

MSC:

11R58 Arithmetic theory of algebraic function fields
11R65 Class groups and Picard groups of orders
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