Non-vanishing elements in finite groups

Many results have been established about determining whether or not an element evaluates to zero on an irreducible character of a group. hi this note it is shown that if a group G has a normal p-subgroup N, and x is an element of N lies in the centre of a Sylow p-subgroup of G, then no irreducible character of G vanishes on x. (C) 2016 Elsevier Inc. All rights reserved.