Abstract If a group G is π-separable, where π is a set of primes, the set of irreducible characters B π ⁡ ( G ) ∪ B π ′ ⁡ ( G ) {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)} can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito–Michler and Thompson’s theorem on character degrees, involving irreducible characters in the set B π ⁡ ( G ) ∪ B π ′ ⁡ ( G ) {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)} .

中文翻译：

---

𝜋-可分离组中的字符度数

摘要 如果群 G 是 π 可分的，其中 π 是素数集，则不可约字符集 B π ⁡ ( G ) ∪ B π ′ ⁡ ( G ) {\operatorname{B}_{\pi}(G )\cup\operatorname{B}_{\pi^{\prime}}(G)} 可以定义。在本文中，我们证明了字符理论中一些经典定理的变体，即 Ito-Michler 定理和 Thompson 字符度定理，涉及集合 B π ⁡ ( G ) ∪ B π ′ ⁡ ( G ) { \operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)} .