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

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

2002-12-20

arxiv.org/abs/math/0212419v1

Mathematics

Number Theory

Scientific paper

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.

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