New results on metric ultraproducts of finite simple groups are established. We show that the isomorphism type of a simple metric ultraproduct of groups $X_{ n_i}(q)$ ($i\in I$) for $X\in\{ { \rm PGL},{ \rm PSp},{ \rm PGO}^{ (\varepsilon)},{ \rm PGU}\}$ ($\varepsilon=\pm$) along an ultrafilter $\mathcal{ U}$ on the index set $I$ for which $n_i\to_{ \mathcal{ U}}\infty$ determines the type $X$ and the field size $q$ up to the possible isomorphism of a metric ultraproduct of groups ${ \rm PSp}_{ n_i}(q)$ and a metric ultraproduct of groups ${ \rm PGO}_{ n_i}^{ (\varepsilon)}(q)$. This extends results of Thom and Wilson.
Categories: math.GR