The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5)

Year 2024, Volume: 2 Issue: 2, 82 - 86, 31.12.2024

Ayoub Basheer Mohammed Basheer , Thekiso Seretlo

https://doi.org/10.26650/ijmath.2024.00018

Abstract

Let 𝐺 be a finite non-abelian simple group and 𝑛𝑋 be a non-trivial conjugacy class of elements of order 𝑛 in 𝐺. We say that 𝐺 is 𝑛𝑋-complementary generated, if for every 𝑥 ∈ 𝐺, there exists an element 𝑦 ∈ 𝑛𝑋 such that 𝐺 = ⟨𝑥, 𝑦⟩ . In this paper we study the 𝑛𝑋-complementary generations for all the non-trivial conjugacy classes of the projective special linear group 𝑃𝑆𝐿(3, 5). We approach this kind of generation using the structure constant method. GAP [The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.9.3; 2018. (http://www.gap-system.org)] is used frequently in our computations.

Keywords

Conjugacy classes, generation, 𝑛𝑋-complementary generation, structure constant

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