Kirillov theory for a class of discrete nilpotent groups

Abstract

This paper is concerned with the Kirillov map for a class of torsion-free nilpotent groups G. G is assumed to be discrete, countable and π-radicable, with π containing the primes less than or equal to the nilpotence class of G. In addition, it is assumed that all of the characters of G have idempotent absolute value. Such groups are shown to be plentiful.