English

The subnormal structure of classical-like groups over commutative rings

K-Theory and Homology 2020-09-08 v1

Abstract

Let nn be an integer greater than or equal to 33 and (R,Δ)(R,\Delta) a Hermitian form ring where RR is commutative. We prove that if HH is a subgroup of the odd-dimensional unitary group U2n+1(R,Δ)U_{2n+1}(R,\Delta) normalised by a relative elementary subgroup EU2n+1((R,Δ),(I,Ω))EU_{2n+1}((R,\Delta),(I,\Omega)), then there is an odd form ideal (J,Σ)(J,\Sigma) such that EU2n+1((R,Δ),(JIk,ΩminJIk+ΣIk))HCU2n+1((R,Δ),(J,Σ))EU_{2n+1}((R,\Delta),(JI^{k},\Omega_{\min}^{JI^k}\overset{\cdot}{+}\Sigma\circ I^{k}))\leq H \leq CU_{2n+1}((R,\Delta),(J,\Sigma)) where k=12k=12 if n=3n=3 respectively k=10k=10 if n4n\geq 4. As a conseqence of this result we obtain a sandwich theorem for subnormal subgroups of odd-dimensional unitary groups.

Keywords

Cite

@article{arxiv.2009.03057,
  title  = {The subnormal structure of classical-like groups over commutative rings},
  author = {Raimund Preusser},
  journal= {arXiv preprint arXiv:2009.03057},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1801.00699

R2 v1 2026-06-23T18:21:33.476Z