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

2003/04/25 by Roland Quême, Roland Queme, Queme, Roland
Computer Science · Mathematics · #11R29 #12F10 #Advanced Mathematical Identities #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R29 #msc:12F10

paper · pdf · doi:10.48550/arxiv.math/0304405

13 pages

arxiv created 2003/04/25 · openalex publication_date 2003/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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× (p^r-1)×(p^r-1-1)× ....× (p-1) and N are not coprime. The proofs are elementary.

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• Some congruences on prime factors of class number of algebraic extensions K/Q
• On the class number of cyclic extensions K/Q
• On prime factors of class number of cyclotomic fields
• On the p-ranks of class groups of certain Galois extensions
• Primes of Higher Degree