Every Abelian Group of Odd Order has a Narcissistic Terrace

Abstract

A recent series of papers by Anderson and Preece has looked at half-and-half terraces for cyclic groups of odd order, particularly focusing on those terraces which are narcissistic. We give a new direct product construction for half-and-half terraces which allows us to construct a narcissistic terrace for every abelian group of odd order. We also show that infinitely many non-abelian groups have narcissistic terraces.