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

Abstract

In [3] it was 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 and point out a version of 'relative' bounded generation results for classical quasisimple groups and its implications on the structure of the lattice of normal subgroups of an ultraproduct of quasisimple groups.

Finitary Approximations of Groups and Their Applications

“…For more details on the algebraic and geometric structure of such ultraproducts see also [54] and [51,58,59]. In view of Proposition 1.7 it is natural to generalize the notion of a C-approximated group to topological groups using ultraproducts: Definition 1.8.…”