A Study of the Number of Roots of xk = g in a Finite Group via Its Frobenius-Schur Indicators

Abstract

Let G be finite group. For [Formula: see text], define [Formula: see text]. This is called the k-th Frobenius-Schur indicator of χ. In this article we study the Frobenius-Schur indicators for Frobenius groups, p-groups, semidihedral groups and modular p-groups. Further, we use this to study the function ζGk(g) which counts the number of roots of [Formula: see text] in a finite group G.