Esther BeneishUniversity of Wisconsin-ParksideMing-chang KangNational Taiwan University
Number Theorymathscidoc:1608.24001
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.
Integral representation, algebraic tori, permutation lattice