Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2013; 50(2): 697-704

Printed March 31, 2013

https://doi.org/10.4134/BKMS.2013.50.2.697

Copyright © The Korean Mathematical Society.

On the solutions of $x^k =g$ in a finite group

Sunil Kumar Prajapati and Ritumoni Sarma

Indian Institute of Technology Delhi, Indian Institute of Technology Delhi

Abstract

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The function $g\mapsto\zeta_G^k(g)$ which counts the number of solutions of $x^k=g$ in a finite group $G$, is not necessarily a character of $G$. We study this function for the case of dihedral groups and generalized quaternion groups.

Keywords: finite groups, group characters

MSC numbers: 20C15

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