P. Hilton et D. Scevenels, Calculating and interpreting the Mislin genus of a special class of nilpotent spaces, P AM MATH S, 127(11), 1999, pp. 3433-3438
We prove that there is a bijection between the Mislin genus of a circle bun
dle over a certain nilpotent base space M, which is constructed from a nilp
otent group N of a certain specified type, and the Mislin genus of N itself
.