Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society

Some connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups

Document Type : Research Paper

Author
S. M. Robati
Department of‎ ‎Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin‎, ‎Iran
Abstract
‎Let $G$ be a finite group‎. ‎We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$‎. ‎In this paper we characterize solvable groups $G$ in which the derived covering number is finite‎.‎ 
Keywords
‎Conjugacy classes‎
irreducible characters‎
solvable groups
Subjects
M. Bianchi, A. G. B. Mauri, M. Herzog, G. Qian and W. Shi, Characterization of nonnilpotent groups with two irreducible character degrees, J. Algebra 284 (2005), no. 1, 326--332.
M. R. Darafsheh and S. M. Robati, Powers of irreducible characters and conjugacy classes in finite groups, J. Algebra Appl. 13 (2014), no. 8, 9 pages.
L. Dornhoff, Group representation theory, Part A: Ordinary representation theory, Marcel Dekker, Inc., New York, 1971.
I. M. Isaacs, Character theory of finite groups, Academic Press, New York-San Francisco-London, 1976.
K. Ishikawa, On finite p-groups which have only two conjugacy lengths, Israel J. Math. 129 (2002) 119--123.
B. Srinivasan, The characters of the finite symplectic group Sp(4; q), Trans. Amer. Math. Soc. 131 (1968) 488--525.
Bulletin of the Iranian Mathematical Society
Volume 42, Issue 1 - Serial Number 1
February 2016
Pages 19-25

  • Receive Date 15 May 2014
  • Revise Date 06 September 2014
  • Accept Date 09 October 2014