Existence of finite groups with classical commutator subgroup

Abstract Given a group G, we may ask whether it is the commutator subgroup of some group G. For example, every abelian group G is the commutator subgroup of a semi-direct product of G x G by a cyclic group of order 2. On the other hand, no symmetric group Sn(n>2) is the commutator subgroup of any group G. In this paper we examine the classical linear groups over finite fields K of characteristic not equal to 2, and determine which can be commutator subgroups of other groups. In particular, we settle the question for all normal subgroups of the general linear groups GLn(K), the unitary groups Un(K) (n≠4), and the orthogonal groups On(K) (n≧7).