## 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 $k$.## References

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## Additional Information

**Sunil K. Chebolu**- Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada
- Email: schebolu@uwo.ca
**J. Daniel Christensen**- Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada
- MR Author ID: 325401
- Email: jdc@uwo.ca
**Ján Mináč**- Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario, Canada
- Email: minac@uwo.ca
- Received by editor(s): October 13, 2006
- Received by editor(s) in revised form: January 2, 2007
- Published electronically: December 6, 2007
- Communicated by: Paul Goerss
- Journal: Proc. Amer. Math. Soc.
**136**(2008), 1171-1179 - MSC (2000): Primary 20C20, 20J06; Secondary 55P42
- DOI: https://doi.org/10.1090/S0002-9939-07-09058-2
- MathSciNet review: 2367091