The hypercentre and the $n$-centre of the unit group of an integral group ring

摘要

In this paper, we first show that the central height of the unit group of the integral group ring of a periodic group is at most $2$. We thengive a complete characterization of the $n$-centre of that unit group. The $n$-centre of the unit group is either the centre or the second centre (for $n geq 2$).