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 & Mahmoud Bashir Alhasanat1 Show affiliations
- Al Hussein Bin Talal University, Jordan
Journal of Mathematics and Statistics, Volume 13, Issue 2, pp. 139–142 · doi.org/10.3844/jmssp.2017.139.142
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.
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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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