On groups with consecutive three smallest character degrees

Abstract

Huppert determined the structure of groups whose degrees are consecutive, then Qian improved that Huppert’s result and showed the structure of finite groups whose degrees of nonlinear characters are consecutive. In this paper, we considered the case when the first three smallest degrees of nonlinear irreducible characters of an almost simple group G are consecutive. Furthermore, Huppert’s conjecture is proved valid for those groups.