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 G and K, must satisfy for the e xistence of a solvable finite group L containing two isomorphic copies of G and H inducing the same permutation character. Also a constructi on of L is given as an iterated wreath product, with respect to their actions on their natural modules, of finite one-dimensional affine gro ups.