Determining group structure from the sets of character degrees

In 1998, Mark Lewis posed a question which would strengthen the connection between the structure of a finite solvable group G and the set of its character degrees. Specifically, Lewis asked the following question:;Lewis' Question: Let G be a solvable group with cd(G)={1, a, b, c, ab, ac}, where a, b, and c are pairwise relatively prime positive integers. Must G = A x B, where cd(A)={1, a} and cd(B)={1, b, c}?;To lend credibility to his question, Lewis verified it if a, b, and c are distinct primes. In this dissertation, we work on the structure of finite solvable groups whose character degree sets are in the form {1, a, b, c, ab, ac}, where a, b, and c are pairwise coprime integers. If p is a prime number and m is a positive integer greater than 1, then we say that the ordered pair (p,m) is a strongly coprime pair if m is not divisible by p and also p does not divide u-1, where 1 = 2, tl in {b, c}, and the Fitting height of G isat most 3.