The Character Zeros And Nonvanishing Elements Of Finite Group

One of the most powerful tools for study of finite groups is the theory of representations and particularly the theory of characters.In this thesis,our main work is as follows.If the finite non-commutative group C is a semidirect product of a cyclic normal subgroup and a cyclic subgroup of prime order,in Chapter 3,we investigate the structure of such groups C,supposing there are just 4 or odd prime zeros of each nonlinear irreducible character out of the normal subgroup.An element s of a finite group G is called nonvanishing element if x(s)≠0 for any irreducible character x of G.In 1999,I.M.Isaacs etc.proved that the nonvanishing elements of a solvable group G are almost in F(G),where F(G)is the fitting subgroup of C.In Chapter 4,we find some nonvanishing elements in finite groups.