Some questions on the class group of cyclotomic fields

Abstract

This article deals with a study of the structure of the class group of the cyclotomic field $K=\Q(ζ_p)$ for $p$ an odd prime number, starting from Stickelberger relation. The present state of this work leads me to set a question for all the prime numbers $h\ne p$ which divide the relative class number $h^{-}(K)$.

The title is modified. The section 4 is removed because it contains an irrecoverable error: It is not possible to use epsilon_chi U_p instead of epsilon_chi U. The section 4 is consequently removed