a new approach to character-free proof for frobenius theorem

Let g be a frobenius group. using character theory, it is proved that the frobenius kernel of g is a normal subgroup of g, which is well-known as a frobenius theorem. there is no known character-free proof for frobenius theorem. in this note, we prove it, by assuming that frobenius groups are non-simple. also, we prove that whether k is a subgroup of g or not, sylow 2-subgroups of g are either cyclic or generalized quaternion group. also by assuming some additional arithmetical hypothesis on g we prove frobenius theorem. we should mention that our proof is character-free.