The ranks of the conjugacy classes of the Symplectic group $Sp(6,2)$

Basheer, A. B. M.; Motalane, M. J.; Seretlo, T. T.

doi:10.22124/jart.2026.30913.1812

The ranks of the conjugacy classes of the Symplectic group $Sp(6,2)$

Articles in Press

Document Type : Research Paper

Authors

¹ School of Mathematical and Computer Sciences‎, ‎University of Limpopo (Turfloop), ‎Sovenga 0727‎, ‎South Africa Mathematics Program‎, ‎Faculty of Education and Arts‎, ‎Sohar University‎,‎ ‎Sohar‎, ‎Oman

² School of Mathematical and Computer Sciences‎, ‎University of Limpopo (Turfloop), ‎Sovenga 0727‎, ‎South Africa

³ Department of Mathematical Sciences‎, ‎North-West University (Mafikeng)‎, ‎Mmabatho 2735‎, ‎South Africa

10.22124/jart.2026.30913.1812

Abstract

Let $G$ be a finite simple group‎, ‎and $X$ be a non-trivial conjugacy class of $G.$ The $rank$ of $X$ in $G$‎, ‎denoted by $rank(G~{:}~X)$‎, ‎is defined to be the minimum number of elements of $X$ generating $G.$ In this paper‎, ‎we investigate the ranks of the non-trivial classes of the symplectic simple group $Sp(6,2).$ We use the structure constants method to determine these ranks‎. ‎The Groups‎, ‎Algorithms and Programming (GAP) \cite{GAP} and the Atlas of finite group representations \cite{Wil} were used in our computations‎.

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