Subgroups of finite solvable groups inducing the same permutation character

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