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

• 来源期刊: 代数集刊（英文版）
• 关键词: Frobenius-Schur indicators p-groups group characters
• 年，卷（期）: 2017,（1）
• 页码范围: 93-108
• 页数: 16页
• 语种: 英文
• DOI: 10.1142/S1005386717000062

摘要

Let G be a finite group.For k ∈ N,x ∈ Irr(G),define cx(k):=1/|G| Σg∈G x(gk).This is called the k-th Frobenius-Schur indicator of x.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 ζG(g) which counts the number of roots of xk =g in a finite group G.