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Restricted Determinantal Homomorphisms and Locally Free Class Groups

Published online by Cambridge University Press:  20 November 2018

Victor Snaith
Victor Snaith*
Affiliation:
McMaster University, Hamilton, Ontario, Canada L8S 4K1
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Let K be a number field and let OK denote the integers of K. The locally free class groups, Cl(OK[G]), furnish a fundamental collection of invariants of a finite group, G. In this paper I will construct some new, non-trivial homomorphisms, called restricted determinants, which map the NGH-invariant idèlic units of Ok([Hab] to Cl(OK[G]). These homomorphisms are constructed by means of the Horn-description of Cl(OK[G]), which describes the locally free class group in terms of the representation theory of G, and the technique of Explicit Brauer Induction, which was introduced in [5].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 4 , 01 August 1990 , pp. 646 - 658
Copyright
Copyright © Canadian Mathematical Society 1990

References

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