We extend Thompson’s theorem by taking into account real-valued irreducible characters. In particular, we prove that if G is a finite group generated by its 2-elements and there is an odd prime p dividing the order of the group G, then there is a non-linear real-valued irreducible character of G of degree coprime to p.

中文翻译：

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汤普森学位定理的真实版本

我们通过考虑实值不可约字符来扩展汤普森定理。特别地，我们证明如果G是一个由其2个元素生成的有限群，并且有一个奇质数p除以群G的阶数，则存在度为素数的G的非线性实值不可约性至p。