A NOTE ON ENNOLA RELATION

Abstract

Ennola gives an example of a relation among the cyclotomic units which is not a combination of elementary relations. He also proves that twice any relation among the cyclotomic units is a consequence of elementary relations. In the sense of the distribution, the torsion part of the universal even punctured distribution $ \big(A_n ^0 \big)^+ $ is a 2-torsion group. In particular, when $n$ has three distinct prime divisors, $ \big(A_n ^0 \big)^+ $ has a unique 2-torsion element. The aim of this paper is to find an algorithm to produce the unique 2-torsion element when $n$ has three distinct odd prime divisors.