Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE SOLUTIONS OF xκ = g IN A FINITE GROUP

  • Received : 2012.01.26
  • Published : 2013.03.31
Download PDF
⟨ Previous Next ⟩

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

Acknowledgement

Supported by : Council of Scientific and Industrial Research (CSIR)

References

  1. R. M. Bryant and L. G. Kovacs, A note on generalized characters, Bull. Aust. Math. Soc. 5 (1971), no. 2, 265-269. https://doi.org/10.1017/S0004972700047146
  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. https://doi.org/10.1007/BF01235344

Cited by

  1. A Study of the Number of Roots of xk = g in a Finite Group via Its Frobenius-Schur Indicators vol.24, pp.01, 2017, https://doi.org/10.1142/S1005386717000062
  2. On the number of solutions of a generalized commutator equation in finite groups vol.156, pp.1, 2018, https://doi.org/10.1007/s10474-018-0863-2