Structure of Groups with At Most Six Character Degrees - Mohammad Hosein Salmani Yengejeh (Journal of Global Pharma Technology, 2018)
Let a, b, c and d be relatively prime integers greater than 1 and cd(G) be the set of all irreducible complex character degrees of a finite group G. Mark Lewis in [4] proved that every group G with cd(G) = 1, p, q, r, pq, pr,where p, q and r are distinct primes, is the direct product of two groups H and K with cd(H)=1, p, q ; cd(K)=1, p, r and so is solvable. We try to use classification of finite groups and drop the primness hypothesis and show that the same result holds in a special case. In fact we show that if a, b, c and d be relatively prime integers greater than 1 and cd(G) 14âŠ†