Groups which do not admit ghosts

Chebolu, Sunil; Christensen, J.; Mináč, Ján

doi:10.1090/S0002-9939-07-09058-2

Groups which do not admit ghosts
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by Sunil K. Chebolu, J. Daniel Christensen and Ján Mináč PDF

Proc. Amer. Math. Soc. 136 (2008), 1171-1179 Request permission

Corrigendum: Proc. Amer. Math. Soc. 136 (2008), 3727-3727.

Abstract:

A ghost in the stable module category of a group $G$ is a map between representations of $G$ that is invisible to Tate cohomology. We show that the only non-trivial finite $p$-groups whose stable module categories have no non-trivial ghosts are the cyclic groups $C_2$ and $C_3$. We compare this to the situation in the derived category of a commutative ring. We also determine for which groups $G$ the second power of the Jacobson radical of $kG$ is stably isomorphic to a suspension of $k$.

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