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

2016/10/12 by Campbell, H. E. A., Chuai, J., Shank, R. J. +1
#13A50 #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1610.03709

Abstract

Suppose \mathbbF is a field of prime characteristic p and E is a finite subgroup of the additive group (\mathbbF,+). Then E is an elementary abelian p-group. We consider two such subgroups, say E and E', to be equivalent if there is an α∈\mathbbF^*:=\mathbbF∖\0\ such that E=αE'. 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.

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