On finitary unitary groups and on the conjecture of Dieudonné (Q1916323)

Let \(F\) be an infinite field of characteristic \(\neq2\) and \(D\) an \(m^2\)-dimensional central division algebra over \(F\) with an involution \(j\neq 1\). Let \(\sum_j(D)\) denote the subgroup of the multiplicative group \(D^*\) generated by the non-zero symmetric elements. The author proves that: If \((V,h)\) is an infinite-dimensional regular unitary space of Witt index at least two over \(D\), then the finitary unitary group \(FU(h)\) is a simple group if and only if \(D^*=\sum_j(D)[D^*,D^*]\). In the non-regular case the author shows that \(FU_0(h)\) is not a simple group, where \(FU_0(h)\) is the subgroup of elements of \(FU(h)\) acting trivially on \(\text{rad}(V,h)\), as normal subgroup.