Representations of elementary abelian p-groups and finite subgroups of fields

Suppose \(\mathbb{F}\) is a field of prime characteristic \(p\) and \(E\) is a finite subgroup of the additive group \((\mathbb{F},+)\). Then \(E\) is an elementary abelian \(p\)-group. We consider two such subgroups, say \(E\) and \(E'\), to be equivalent if there is an \(\alpha\in\mathbb{F}^*...

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Bibliographic Details
Published inarXiv.org
Main Authors Campbell, H E A, Chuai, J, Shank, R J, Wehlau, D L
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.08.2018
Subjects
Equivalence
Rational functions
Subgroups
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Summary:Suppose \(\mathbb{F}\) is a field of prime characteristic \(p\) and \(E\) is a finite subgroup of the additive group \((\mathbb{F},+)\). Then \(E\) is an elementary abelian \(p\)-group. We consider two such subgroups, say \(E\) and \(E'\), to be equivalent if there is an \(\alpha\in\mathbb{F}^*:=\mathbb{F}\setminus\{0\}\) such that \(E=\alpha E'\). In this paper we show that rational functions can be used to distinguish equivalence classes of subgroups and, for subgroups of prime rank or rank less than twelve, we give explicit finite sets of separating invariants.
ISSN:2331-8422