Abstract
For a character χ of a finite group G, it is known that the product sh(χ) = Πl∈L(χ(1) - l) is a multiple of |G|,where L is the image of χ on G -{1}. χ is said to be a sharp character of type L if sh(χ) =|G|. This is a generalization of the permutation characters of sharp permutation groups. Without loss of generality, we may assume that (χ, 1G)G = 0. In this paper, we classify the finite groups with sharp characters of type {l, l + p} for an odd prime p under the additional hypothesis Z(G) > 1 and (χ, χ)G = p.
