On unitary groups modulo infinitesimals Original Research Article

We deal with a hermitian space V over an involutorial division ring D with characteristic not 2 and with a nontrivial nonarchimedean valuation. We are concerned with the group C of unitary transformations modulo the subgroup 1 + J (J is the ideal of nonunits of the valuation ring in D). The normal subgroup structure of C is studied. It is also shown that the group C of a hyperbolic space is generated by certain standard matrices.