Connective $\mathrm{Im}(J)$–theory for cyclic groups

Abstract

We study connective $Im\left(J\right)$–theory for the classifying space $B\mathbb{Z}∕p^a$ of a finite cyclic $p$–group and compute the $Im\left(J\right)$–cohomology groups completely. We also compute the $Im\left(J\right)$–homology groups, with the exception of a finite range of dimensions.