The ranks of the classes of the Chevalley group $G_{2}(4)$

نویسندگان
Motalane, Malebogo John ID 1
Sehoana, Mahlare G ID 2
Seretlo, Thekiso Trevor ID 3
Basheer, Ayoub Basheer Mohammed ID 4

1 School of Mathematical and Computer Sciences, University of Limpopo (Turfloop) P Bag X1106, Sovenga 0727, South Africa.

2 School of Mathematical and Computer Sciences, University of Limpopo (Turfloop) P Bag X1106, Sovenga 0727, South Africa.

3 School of Mathematical and Statistical Sciences, PAA Focus Area, North-West University (Mahikeng) P. Bag X2046, Mmabatho 2735, South Africa.

4 School of Mathematical and Computer Sciences, University of Limpopo (Turfloop), P Bag X1106, Sovenga 0727, South Africa

doi
10.22034/as.2025.21872.1730
چکیده

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 minimal number of elements of $X$ generating $G$. In this paper we establish the ranks of all the conjugacy classes of elements for Chevalley group $G_{2}(4)$ using the structure constants method. The Groups, Algorithms and Programming, GAP [14] is used frequently in our computations.

کلیدواژه‌ها
Chevalley group, conjugacy class, Rank, Structure constant