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