Some congruences on prime factors of class number of finite algebraic extensions K/Q

الأصل · EN

This paper is a contribution to the description of some congruences on the odd prime factors of the class number of the number fields. An example of results obtained is: Let L/Q be a finite Galois solvable extension with [L:Q]=N, where N > 1 is odd. Let h(L) be the class number of L. Suppose that h(L) > 1. Let p be a prime dividing h(L). Let r be the rank of the p-class group of L. Then the product p× (pʳ-1)×(pʳ⁻¹-1)×....× (p-1) and N are not coprime. The proofs are elementary.