A Theorem on Factorizable Groups of Odd Order

Recently, W. Feit [2] obtained some results on factorizable groups of odd order. By using his procedure and applying the theory of R. Brauer [1], we can prove the following theorem similar to that of W. Feit [2]: Theorem. Let G be a factorizable group of odd order such that G = HM where H is a subgroup of order 3p, p being a prime greater than 3, and M is a maximal subgroup of G. Then G contains a proper normal subgroup which is contained either in H or in M.