  In this short note we study the topological Hoschschild homology of
Eilenberg-MacLane spectra for finite cyclic groups. In particular, we show that
the Eilenberg-MacLane spectrum H(Z/p^k) is a Thom spectrum for any prime p
(except, possibly, when p=k=2) and we also compute its topological Hoschshild
homology. This yields a short proof of the results obtained by Brun, and by
Pirashvili except for the anomalous case p=k=2.
