Some congruences on prime factors of class number of algebraic   extensions K/Q
  This paper is an updated version of ANT-0372 (2002 dec 4) with the same title. Several errors are corrected in this version.   An example of the kind of results obtained is: Let K/\Q be an abelian extension with N = [K:\Q] > 1, N odd. Let h(K) be the class number of K. Suppose that h(K) > 1. Let p be a prime dividing h(K). Let r_p be the rank of the p-class group of K. Then p \times (p^{r_p}-1) and N are not coprime.   The paper is at elementary level and contains a lot of numerical examples. 
Roland Queme