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- Title
PROJECTIVE CHARACTERS WITH PRIME POWER DEGREES.
- Authors
LIU, YANG
- Abstract
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.
- Subjects
FINITE groups; MEASUREMENT of angles (Geometry); REPRESENTATION theory; IRREDUCIBLE polynomials; MATHEMATICS theorems
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 1, p78
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718000825