An Upper Bound to the Number of Conjugacy Classes of Non-Abelian Nilpotent Groups
Bilal Al-Hasanat, Awni Al-Dababseh, E. Al-Sarairah, Sadoon Alobiady and Mahmoud Bashir Alhasanat
DOI : 10.3844/jmssp.2017.139.142
Journal of Mathematics and Statistics
Volume 13, Issue 2
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.
© 2017 Bilal Al-Hasanat, Awni Al-Dababseh, E. Al-Sarairah, Sadoon Alobiady and Mahmoud Bashir Alhasanat. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.