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

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

2003-04-25

arxiv.org/abs/math/0304405v1

Mathematics

Number Theory

13 pages

Scientific paper

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\times (p^r-1)\times(p^{r-1}-1)\times ....\times (p-1) and N are not coprime. The proofs are elementary.

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