摘要
Let G be a finite group. For k ∈ N, X ∈ Irr（G）, define c（k）x ：= 1/G ∑g∈G x（gk）. This is called the k-th Frobenius-Schur indicator of X. In this article we study the Probenius-Schur indicators for Frobenius groups, p-groups, semidihedral groups and mod- ular p-groups. Further, we use this to study the function ζ kG（g） which counts the number of roots of xk = g in a finite group G.
Let G be a finite group. For k ∈ N, X ∈ Irr（G）, define c（k）x ：= 1/G ∑g∈G x（gk）. This is called the k-th Frobenius-Schur indicator of X. In this article we study the Probenius-Schur indicators for Frobenius groups, p-groups, semidihedral groups and mod- ular p-groups. Further, we use this to study the function ζ kG（g） which counts the number of roots of xk = g in a finite group G.
