## Generic central extensions and projective representations of finite groups

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- by Rachel Quinlan PDF
- Represent. Theory
**5**(2001), 129-146 Request permission

## Abstract:

Any free presentation for the finite group $G$ determines a central extension $(R,F)$ for $G$ having the projective lifting property for $G$ over any field $k$. The irreducible representations of $F$ which arise as lifts of irreducible projective representations of $G$ are investigated by considering the structure of the group algebra $kF$, which is greatly influenced by the fact that the set of torsion elements of $F$ is equal to its commutator subgroup and, in particular, is finite. A correspondence between projective equivalence classes of absolutely irreducible projective representations of $G$ and $F$-orbits of absolutely irreducible characters of $F’$ is established and employed in a discussion of realizability of projective representations over small fields.## References

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## Additional Information

**Rachel Quinlan**- Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
- Address at time of publication: Department of Mathematics, University College Dublin, Dublin, Ireland
- Email: rachel.quinlan@ucd.ie
- Received by editor(s): February 26, 2001
- Received by editor(s) in revised form: March 23, 2001
- Published electronically: June 5, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Represent. Theory
**5**(2001), 129-146 - MSC (2000): Primary 20C25; Secondary 20C07
- DOI: https://doi.org/10.1090/S1088-4165-01-00122-4
- MathSciNet review: 1835002