Subgroups of finite soluble groups inducing the same permutation character

In this paper there are found necessary and sufficient conditions that a pair of solvable finite groups, say and , must satisfy for the existence of a solvable finite group containing two isomorphic copies of and inducing the same permutation character. Also a construction of is given as an iterated wreath product, with respect to their actions on their natural modules, of finite one-dimensional affine groups.