Overgroups of SU(n,K,f) or \(\Omega\) (n,K,Q) in GL(n,K)
Let K be a division ring with involution, f an isotropic hermitian or skew-hermitian even (trace-valued) form on an n-dimensional left K-vector space, \(n\geq 3\), \(N=SU(n,K,f)\) the subgroup of the unitary group generated by transvections. Theorem 1 asserts that every subgroup X of GL(n,K) containing N either normalizes N or contains SL(n,K). Theorem 2 asserts a similar result for orthogonal groups over commutative K (which differ from the corresponding unitary groups in the case \(2K=0)\).
scientific article; zbMATH DE number 4136226