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PROJECTIVE CHARACTERS WITH PRIME POWER DEGREES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 99 / Issue 1 / February 2019
- Published online by Cambridge University Press:
- 28 August 2018, pp. 78-82
- Print publication:
- February 2019
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- Article
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We consider the relationship between structural information of a finite group
$G$ and 
$\text{cd}_{\unicode[STIX]{x1D6FC}}(G)$, the set of all irreducible projective character degrees of 
$G$ with factor set 
$\unicode[STIX]{x1D6FC}$. We show that for nontrivial 
$\unicode[STIX]{x1D6FC}$, if all numbers in 
$\text{cd}_{\unicode[STIX]{x1D6FC}}(G)$ are prime powers, then 
$G$ is solvable. Our result is proved by classical character theory using the bijection between irreducible projective representations and irreducible constituents of induced representations in its representation group.
