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On a question of Dixon and Rahnamai Barghi. (English) Zbl 07072599
Summary: Let $$G$$ be a finite non-solvable group with a primitive irreducible character $$\chi$$ that vanishes on one conjugacy class. We show that $$G$$ has a homomorphic image that is either almost simple or a Frobenius group. We also classify such groups $$G$$ with a composition factor isomorphic to a sporadic group, an alternating group $$A_n$$, $$n\geq 5$$ or $$\mathrm{PSL}_2(q)$$, where $$q\geq 4$$ is a prime power, when $$\chi$$ is faithful. Our results partially answer a question of Dixon and Rahnamai Barghi.

##### MSC:
 20C15 Ordinary representations and characters
Full Text:
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