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On Schur 3-groups
Let be a finite group. If is a permutation group with
and is the set of orbits of the
stabilizer of the identity in , then the
-submodule
of
the group ring is an -ring as it was observed by Schur.
Following P\"{o}schel an -ring over is said to be schurian
if there exists a suitable permutation group such that
. A finite group is called a Schur group
if every -ring over is schurian. We prove that the groups
, where
, are not Schur. Modulo previously obtained results, it follows that
every Schur -group is abelian whenever is an odd prime.Comment: 8 page
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