Some Results on Finite Groups Whose Order Contains a Prime to the First Power
نویسندگان
چکیده
In a previous investigation [1], the author has studied finite groups © of an order g = pgo where p is a prime and go an integer not divisible by p. This work has been continued by H. F. Tuan [51 Let t denote the number of conjugate classes of ® which consist of element of order p. Tuan dealt with the groups ® for which t^2 and which have a faithful representation of degree less than p 1. We shall assume here that ί>3.** We shall also suppose that ® does not have a normal subgroup of order p. We state here two results. We shall show (Corollary, Theorem 1) that if 7 is a faithful irreducible character of ® of degree n which has T > 1 conjugates over the field of the go-th roots of unity, then
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