Almost Simple Groups With At Most Nine Special Irreducible Character degrees

Let a, b, c, and d be pairwise relatively prime integers greater than 1 and cd(G) be the set of all irreducible complex character degree of a finite group G. In this paper, by using the Classification of Finite Simple Groups we find all almost simple groups G with cd(G) ⊆ {1, a, b, c, d, ac, ad, bc, bd}. In particular we show that there exists an integer f ≥ 2such that {2f − 1, 2f } ⊆ cd(G).

کلیدواژه ها:

Character degree ، Solvable groups ، Almost simple groups