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# Kirillov Theory for a Class of Discrete Nilpotent Groups

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 $\pi$-radicable, with $\pi$ 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.