Veeru Devgan works in Hollywood.
In mathematics , in the area of algebra known as group theory , an imperfect group is a group with no nontrivial perfect quotients .. mathematics. mathematics. algebra. algebra. group theory. group theory. group. group ( mathematics ). perfect. perfect group. quotients. quotient group. Some of their basic properties were established in .. The study of imperfect groups apparently began in .. The class of imperfect groups is closed under extension and quotient groups , but not under subgroups .. extension. group extension. If G is a group , N , M are normal subgroups with G / N and G / M imperfect , then G  /  -LRB- N ∩ M -RRB- is imperfect , showing that the class of imperfect groups is a formation .. group. group ( mathematics ). formation. Carter subgroup#Generalizations. The -LRB- restricted or unrestricted -RRB- direct product of imperfect groups is imperfect .. direct product. direct product of groups. Every solvable group is imperfect .. group. group ( mathematics ). solvable group. solvable group. Finite symmetric groups are also imperfect .. The general linear groups PGL -LRB- 2 , q -RRB- are imperfect for q an odd prime power .. For any group H , the wreath product H wr Sym2 of H with the symmetric group on two points is imperfect .. group. group ( mathematics ). symmetric group. symmetric group. wreath product. wreath product. In particular , every group can be embedded as a two-step subnormal subgroup of an imperfect group of roughly the same cardinality -LRB- 2  |  H  |  2 -RRB- .. group. group ( mathematics ). subgroup. subgroup. subnormal subgroup. subnormal subgroup