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- W2622659176 abstract "A proof of a theorem of M. Hertweck presented during a seminar in January 2013 in Stuttgart is given. The proof is based on a preprint given to me by Hertweck. Let $R$ be a commutative ring, $G$ a finite group, $N$ a normal $p$-subgroup of $G$ and denote by $RG$ the group ring of $G$ over $R$. It is shown that a torsion unit $u$ in $mathbb{Z}G$ mapping to the identity under the natural homomorphism $mathbb{Z}G rightarrow mathbb{Z}G/N$ is conjugate in the unit group of $mathbb{Z}_pG$ to an element in $N$. Here $mathbb{Z}_p$ denotes the $p$-adic integers. The result is achieved proving a result in the context of the so-called double action formalism for group rings over $p$-adic rings. This widely generalizes a theorem of Hertweck and a related theorem by Caicedo-Margolis-del Rio and has consequences for the study of the Zassenhaus Conjecture for integral group rings." @default.
- W2622659176 created "2017-06-15" @default.
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- W2622659176 date "2017-06-07" @default.
- W2622659176 modified "2023-09-27" @default.
- W2622659176 title "A theorem of Hertweck on $p$-adic conjugacy of $p$-torsion units in group rings" @default.
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