Abstract Let G be a finite transitive permutation group of degree n, with point stabilizer H ≠ 1 {H\neq 1} and permutation character π. For every positive integer t, we consider the generalized character ψ t = ρ G - t ⁢ ( π - 1 G ) {\psi_{t}=\rho_{G}-t(\pi-1_{G})} , where ρ G {\rho_{G}} is the regular character of G and 1 G {1_{G}} the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that ψ t {\psi_{t}} is a character of G. A necessary condition is that t ≤ min ⁡ { n - 1 , | H | } {t\leq\min\{n-1,\lvert H\rvert\}} , and it turns out that ψ t {\psi_{t}} is a character of G for t = n - 1 {t=n-1} resp. t = | H | {t=\lvert H\rvert} precisely when G is 2-transitive resp. a Frobenius group.

中文翻译：

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一些与传递置换群相关的广义字符

摘要 设 G 为 n 次有限传递置换群，点稳定器 H ≠ 1 {H\neq 1}，置换特征为 π。对于每个正整数 t，我们考虑广义字符 ψ t = ρ G - t ⁢ ( π - 1 G ) {\psi_{t}=\rho_{G}-t(\pi-1_{G})} ，其中 ρ G {\rho_{G}} 是 G 的正则字符，1 G {1_{G}} 是 1 字符。我们给出 t（和 G）的充分必要条件，保证 ψ t {\psi_{t}} 是 G 的一个字符。一个必要条件是 t ≤ min ⁡ { n - 1 , | H | } {t\leq\min\{n-1,\lvert H\rvert\}} ，结果 ψ t {\psi_{t}} 是 G 的一个字符，对于 t = n - 1 {t= n-1} 分别 t = | H | {t=\lvert H\rvert} 恰好当 G 是 2-transitive resp 时。Frobenius 群。