3 research outputs found
On the -divisibility of even -groups of the ring of integers of a cyclotomic field
Let be a given positive odd integer and an odd prime. In this paper,
we shall give a sufficient condition when a prime divides the order of the
groups and
, where is a primitive th root of
unity. When is a -extension contained in for some
prime , we also establish a necessary and sufficient condition for the order
of to be divisible by . This generalizes a
previous result of Browkin which in turn has applications towards establishing
the existence of infinitely many cyclic extensions of degree which are -rational