Overgroups of $E(m,R)⊗E(n,R)$ I. Levels and normalizers
Overgroups of $E(m,R)⊗E(n,R)$ I. Levels and normalizers
The study of subgroups $H$ such that \[ E(m,R)\otimes E(n,R)\le H\le G=\operatorname {GL}(mn,R) \] is started, provided that the ring $R$ is commutative and $m,n\ge 3$. The principal results of this part can be summarized as follows. The group $\operatorname {GL}_m\otimes \operatorname {GL}_n$ is described by equations, and it is …