The subnormal structure of classical-like groups over commutative rings (Q831199)

In the article under review, the author studies the subgroup structure of the odd-dimensional unitary group \(U_{2n+1}(R, \Delta)\), where \((R, \Delta)\) is a Hermitian form ring (\(R\) is commutative ring). Among these results, it is proved that if \(H\) is a subgroup of \(U_{2n+1}(R, \Delta)\) normalized by a relative elementary subgroup \(EU_{2n+1}((R, \Delta), (I, \Omega))\), then there is an odd-form ideal \((J, \Sigma)\) such that \[EU_{2n+1}((R, \Delta), (JI^k, \Omega_{min}^{JI^k}\dot+\Sigma\circ I^k))\le H\le CU_{2n+1}((R, \Delta), (J, \Sigma)),\] where \(k=12\) if \(n=3\) respectively \(k=10\) if \(n\ge 4\). As a consequence of this result, a sandwich theorem for subnormal subgroups of odd-dimensional unitary group is obtained.