LAUSR

Abstract New results on metric ultraproducts of finite simple groups are established. We show that the isomorphism type of a simple metric ultraproduct of groups Xni⁢(q){X_{n_{i}}(q)} (i∈I{i\in I}) for X∈{PGL,PSp,PGO(ε),PGU}{X\in\{\operatorname{PGL},\operatorname{PSp},\operatorname{PGO}^{(\varepsilon)% },\operatorname{PGU}\}} (ε=±{\varepsilon=\pm}) along an ultrafilter ????{\mathcal{U}} on the index set I for which ni→????∞{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 PSpni⁡(q){\operatorname{PSp}_{n_{i}}(q)} and a metric ultraproduct of groups PGOni(ε)⁡(q){\operatorname{PGO}_{n_{i}}^{(\varepsilon)}(q)}. This extends results of [A. Thom and J. Wilson, Metric ultraproducts of finite simple groups, Comp. Rend. Math. 352 2014, 6, 463–466].