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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
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