Some Results on Finite Groups Whose Order Contains a Prime to the First Power
- 1 July 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 27 (2) , 381-399
- https://doi.org/10.1017/s0027763000026246
Abstract
In a previous investigation [1], the author has studied finite groups of an order g = pg0 where p is a prime and g0 an integer not divisible by p. This work has been continued by H. F. Tuan [5]. 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 t≧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 / is a faithful irreducible character of of degree n which has T>1 conjugates over the field of the g0-th roots of unity, thenKeywords
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