Research Article Open Access

An Upper Bound to the Number of Conjugacy Classes of Non-Abelian Nilpotent Groups

Bilal Al-Hasanat1, Awni Al-Dababseh1, E. Al-Sarairah1, Sadoon Alobiady1 and Mahmoud Bashir Alhasanat1
  • 1 Al Hussein Bin Talal University, Jordan

Abstract

The number of conjugacy classes of symmetric group, dihedral group and some nilpotent groups is obtained. Until now, it has not been obtained for all nilpotent groups. Although there are some lower bounds to this value, there is no non-trivial upper bound. This paper aims to investigate an upper bound to this number for all finite nilpotent groups. Moreover, the exact number of conjugacy classes is found for a certain case of non-abelian nilpotent groups.

Journal of Mathematics and Statistics
Volume 13 No. 2, 2017, 139-142

DOI: https://doi.org/10.3844/jmssp.2017.139.142

Submitted On: 22 June 2016 Published On: 23 May 2017

How to Cite: Al-Hasanat, B., Al-Dababseh, A., Al-Sarairah, E., Alobiady, S. & Alhasanat, M. B. (2017). An Upper Bound to the Number of Conjugacy Classes of Non-Abelian Nilpotent Groups. Journal of Mathematics and Statistics, 13(2), 139-142. https://doi.org/10.3844/jmssp.2017.139.142

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Keywords

  • Conjugacy Class
  • Centre
  • Nilpotent Class