Similarly to the Frobenius–Schur indicator of irreducible characters, we consider higher Frobenius–Schur indicators $\nu _{p^n}(\chi ) = |G|^{-1} \sum _{g \in G} \chi (g^{p^n})$ for primes p and $n \in \mathbb {N}$ , where G is a finite group and $\chi $ is a generalised character of G. These invariants give answers to interesting questions in representation theory. In particular, we give several characterisations of groups via higher Frobenius–Schur indicators.

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关于更高 FROBENIUS-SCHUR 指标

与不可约字符的 Frobenius–Schur 指标类似，我们考虑更高的 Frobenius–Schur 指标 $\nu _{p^n}(\chi ) = |G|^{-1} \sum _{g \in G} \ chi (g^{p^n})$ 对于素数p和 $n \in \mathbb {N}$ ，其中G是有限群， $\chi $ 是G的广义特征。这些不变量给出了表示论中有趣问题的答案。特别是，我们通过更高的 Frobenius-Schur 指标给出了组的几个特征。