The subnormal structure of classical-like groups over commutative rings

Raimund Preusser 1
  • 1 Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
Raimund Preusser

Abstract

Let 𝑛 be an integer greater than or equal to 3, and let (R,Δ) be a Hermitian form ring, where 𝑅 is commutative. We prove that if 𝐻 is a subgroup of the odd-dimensional unitary group U2n+1(R,Δ) normalised by a relative elementary subgroup EU2n+1((R,Δ),(I,Ω)), then there is an odd form ideal (J,Σ) such that

EU2n+1((R,Δ),(JIk,ΩminJIkΣIk))HCU2n+1((R,Δ),(J,Σ)),

where k=12 if n=3 respectively k=10 if n4. As a consequence of this result, we obtain a sandwich theorem for subnormal subgroups of odd-dimensional unitary groups.

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