Normal subgroups of symplectic groups over rings

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Abstract

We consider a module with an alternating form over a commutative ring. Under certain conditions, which hold, for example, when the form is nonsingular and the module is projective of rank ≥ 6 and contains a unimodular vector, we describe all subgroups of the symplectic group which are normalized by symplectic transvections. This generalizes many previous results of Dickson, Klingenberg, Abe, Bak, et al.

Original languageEnglish (US)
Pages (from-to)647-673
Number of pages27
JournalK-Theory
Volume2
Issue number5
DOIs
StatePublished - Sep 1 1989

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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