  Theorem. Let $\pi$ be a finite group of order $n$, $R$ be a Dedekind domain
satisfying that (i) $\fn{char}R=0$, (ii) every prime divisor of $n$ is not
invertible in $R$, and (iii) $p$ is unramified in $R$ for any prime divisor $p$
of $n$. Then all the flabby (resp.\ coflabby) $R\pi$-lattices are invertible if
and only if all the Sylow subgroups of $\pi$ are cyclic. The above theorem was
proved by Endo and Miyata when $R=\bm{Z}$ \cite[Theorem 1.5]{EM}. As
applications of this theorem, we give a short proof and a partial
generalization of a result of Torrecillas and Weigel \cite[Theorem A]{TW},
which was proved using cohomological Mackey functors.
