On the nX-complementary generations of a Chevalley group

A finite non-abelian group G is said to be nX-complementary generated if, for any arbitrary non-identity element x G, there exists an element y nX such that G = x, y, where nX is a non-trivial conjugacy class of elements of order n.In this paper, we classify all the non-trivial conjugacy classes of the Chevalley group G2(4), determining whether they are complementary generators of G2(4) or not.We prove that the group G2( 4) is nX-complementary generated if and only if n 5 and nX / {5A, 5B}.

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Publication Details

Journal
Electronic Journal of Mathematics
Published
2025-09-04
DOI
https://doi.org/10.47443/ejm.2025.028
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
article
Field-Weighted Citation Impact
0.00

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article

On the nX-complementary generations of a Chevalley group

Ayoub B. M. Basheer, Malebogo John Motalane, Mahlare Gerald Sehoana, Thekiso Trevor Seretlo
Electronic Journal of Mathematics
Advanced Differential Equations and Dynamical Systems
article

On the nX-complementary generations of a Chevalley group

Ayoub B. M. Basheer, Malebogo John Motalane, Mahlare Gerald Sehoana, Thekiso Trevor Seretlo
article en

Abstract

A finite non-abelian group G is said to be nX-complementary generated if, for any arbitrary non-identity element x G, there exists an element y nX such that G = x, y, where nX is a non-trivial conjugacy class of elements of order n.In this paper, we classify all the non-trivial conjugacy classes of the Chevalley group G2(4), determining whether they are complementary generators of G2(4) or not.We prove that the group G2( 4) is nX-complementary generated if and only if n 5 and nX / {5A, 5B}.

Electronic Journal of MathematicsVol. 10
National Research Foundation, North-West University, Sohar University
Openalex Percentile: Top 71%
Advanced Differential Equations and Dynamical Systems
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