On The Relative Class Number of Special Cyclotomic Fields

Abstract

Let p be an odd prime, p be a primitive pth root of unity and h������p be the relative class number of the pth cyclotomic fi eld Q( p) over the rationals Q defi ned by p. The main purpose of this paper is to discuss arithmetic properties of factors of h������p for an odd prime p of the form p = 4q + 1 with q a prime.