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- W2073485676 abstract "The Dade group D ( P ) of a finite p -group P , formed by equivalence classes of endo-permutation modules, is a finitely generated Abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of P and it is conjectured that every non-trivial element of its torsion subgroup D t ( P ) has order 2, (or also 4, in case p =2). The group D t ( P ) is closely related to the injectivity of the restriction map Res :T(P)→∏ E T(E) , where E runs over elementary Abelian subgroups of P and T ( P ) denotes the group of equivalence classes of endo-trivial modules, which is still unknown for (almost) extra-special groups ( p odd). As metacyclic p -groups have no (almost) extra-special section, we can verify the above conjecture in this case. Finally, we compute the whole Dade group of a metacyclic p -group." @default.
- W2073485676 created "2016-06-24" @default.
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- W2073485676 date "2003-08-01" @default.
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- W2073485676 title "The Dade group of a metacyclic p-group" @default.
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- W2073485676 doi "https://doi.org/10.1016/s0021-8693(03)00328-4" @default.
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