Finite quotients of ultraproducts of finite perfect groups

Groups that can be approximated by finite groups have been the subject of extensive research. This has led to the investigations of the subgroups of algebraic ultraproducts of finite groups, i.e., LEF groups. This paper addresses the dual problem: what are the abstract quotients of ultraproducts of finite groups? Certain cases were already well-studied. For example, if we have an ultraproduct of solvable group, then it is well-known that any finite abstract quotients must still be solvable. This paper studies the case of ultraproducts of finite perfect groups. We shall show that any finite group could be a quotient of an ultraproduct of finite perfect groups. We provide an explicit construction on how to achieve this for each finite group. & COPY; 2023 Elsevier Inc. All rights reserved.