A note on the normal subgroup lattice of ultraproducts of finite quasisimple groups

Abstract

Abel Stolz and Andreas Thom [Proc. Lond. Math. Soc. 108 (2014), pp. 73–102] stated that the lattice of normal subgroups of an ultraproduct of finite simple groups is always linearly ordered. This is false in this form in most cases for classical groups of Lie type. We correct the statement in this case and point out a version of \enquote*relative bounded normal generation for classical quasisimple groups and its implications on the structure of the lattice of normal subgroups of an ultraproduct of such groups.