Browse > Article
http://dx.doi.org/10.4134/BKMS.2013.50.2.697

ON THE SOLUTIONS OF xκ = g IN A FINITE GROUP  

Prajapati, Sunil Kumar (Department of Mathematics Indian Institute of Technology Delhi)
Sarma, Ritumoni (Department of Mathematics Indian Institute of Technology Delhi)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 697-704 More about this Journal
Abstract
The function $g{\mapsto}{\zeta}^k_G(g)$ 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;
Citations & Related Records
연도 인용수 순위
  • Reference
1 R. M. Bryant and L. G. Kovacs, A note on generalized characters, Bull. Aust. Math. Soc. 5 (1971), no. 2, 265-269.   DOI
2 C. W. Charles and I. Reiner, Methods of Representation Theory. Vol. II, With applications to finite groups and orders, John Wiley & Sons Inc., New York, 1987.
3 I. M. Isaacs, Character Theory of Finite Groups, AMS Chelsea Publishing, Academic Press, New York, 2000.
4 A. Kerber and B. Wagner, Gleichungen in endlichen Gruppen, Arch. Math. (Basel) 35 (1980), no. 3, 252-262.   DOI