  Let p > 2 be a prime. Let Q(zeta) be the p-cyclotomic field. Let pi be the
prime ideal of Q(zeta) lying over p. This article aims to describe some pi-adic
congruences characterizing the structure of the p-class group and of the unit
group of the field Q(zeta). For the unit group, this article supplements the
1954 and 1956 papers of Denes on this topic. A complete summarizing of the
results obtained follows in the Introduction section of the paper (pages 3 to
6). This new version of the article with the same title, submitted with
reference math.NT/0407430 25 Jul 2004: - corrects several typing errors in the
introduction and in the paper, - simplifies some proofs of pi-adic congruences
connected to p-class group, - removes the section dealing of the singular group
foreseen in an independant paper.
