论文标题
在交换环上类似古典基团的亚正常结构
The subnormal structure of classical-like groups over commutative rings
论文作者
论文摘要
让$ n $成为一个大于或等于$ 3 $和$（r，δ）$的整数，而$ r $是可交换的。我们证明，如果$ h $是奇数统一组的子组$ u_ {2n+1}（r，δ）$，由相对基本亚组$ eu_ {2n+1}（（r，Δ），（i，ω），（i，ω））$归一化，那么有一个奇数的理想$（j，j，j，j，j，j，j，n f） $ eu_ {2n+1}（（（r，δ），（ji^{k}，ω_ {\ min}^{ji^k} \ overset {\ cdot} {+} {+}σ $ k = 12 $如果$ n = 3 $ $ k = 10 $如果$ n \ geq 4 $。作为此结果的共同点，我们获得了奇数单位基团的亚平方亚组的三明治定理。
Let $n$ be an integer greater than or equal to $3$ and $(R,Δ)$ a Hermitian form ring where $R$ is commutative. We prove that if $H$ is a subgroup of the odd-dimensional unitary group $U_{2n+1}(R,Δ)$ normalised by a relative elementary subgroup $EU_{2n+1}((R,Δ),(I,Ω))$, then there is an odd form ideal $(J,Σ)$ such that $EU_{2n+1}((R,Δ),(JI^{k},Ω_{\min}^{JI^k}\overset{\cdot}{+}Σ\circ I^{k}))\leq H \leq CU_{2n+1}((R,Δ),(J,Σ))$ where $k=12$ if $n=3$ respectively $k=10$ if $n\geq 4$. As a conseqence of this result we obtain a sandwich theorem for subnormal subgroups of odd-dimensional unitary groups.
