RESEARCH ANNOUNOEMENTS

Let G be a finite group, Irr(G) denotes the set of irreducible complex characters of G and gGthe conjugacy class of G containing element g. A well-known theorem of Burnside(1,Theorem3. 15]) states that every nonlinear X E Irr(G) has a zero on G, that is, an element x (or a conjugacyclass xG) of G with x(x) = 0. So, if the number of zeros of character table is very small, we mayexpect, the structure of group is heavily restricted. For example, 2, Proposition 2.7] claimesthat G is a Fro…