The Gorenstein property for modular binary forms invariants

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Let G⊆SL(2, F) be a finite group, V=F2 the natural SL(2, F)-module, and charF=p>0. Let S(V) be the symmetric algebra of V and S(V)G the ring of G-invariants. We provide examples of groups G, where S(V)G is Cohen-Macaulay, but is not Gorenstein. This refutes a natural conjecture due to Kemper, Körding, Malle, Matzat, Vogel and Wiese. Let T(G) denote the subgroup generated by all transvections of G. We show that S(V)G is Gorenstein if and only if one of the following cases holds:(1)T(G)={1G},(2)V is an irreducible T(G)-module,(3)V is a reducible T(G)-module and |G| divides |T(G)|(|T(G)|-1).

Original languageEnglish
Pages (from-to)232-247
Number of pages16
JournalJournal of Algebra
StatePublished - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.


  • Gorenstein
  • Modular invariants

ASJC Scopus subject areas

  • Algebra and Number Theory


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