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DOI :10.26650/ijmath.2024.00018   IUP :10.26650/ijmath.2024.00018    Full Text (PDF)

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

Ayoub Basheer, Thekiso Seretlo

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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APA

Basheer, A., & Seretlo, T. (2024). The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics, 2(2), 82-86. https://doi.org/10.26650/ijmath.2024.00018


AMA

Basheer A, Seretlo T. The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics. 2024;2(2):82-86. https://doi.org/10.26650/ijmath.2024.00018


ABNT

Basheer, A.; Seretlo, T. The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics, [Publisher Location], v. 2, n. 2, p. 82-86, 2024.


Chicago: Author-Date Style

Basheer, Ayoub, and Thekiso Seretlo. 2024. “The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5).” Istanbul Journal of Mathematics 2, no. 2: 82-86. https://doi.org/10.26650/ijmath.2024.00018


Chicago: Humanities Style

Basheer, Ayoub, and Thekiso Seretlo. “The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5).” Istanbul Journal of Mathematics 2, no. 2 (Feb. 2025): 82-86. https://doi.org/10.26650/ijmath.2024.00018


Harvard: Australian Style

Basheer, A & Seretlo, T 2024, 'The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5)', Istanbul Journal of Mathematics, vol. 2, no. 2, pp. 82-86, viewed 5 Feb. 2025, https://doi.org/10.26650/ijmath.2024.00018


Harvard: Author-Date Style

Basheer, A. and Seretlo, T. (2024) ‘The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5)’, Istanbul Journal of Mathematics, 2(2), pp. 82-86. https://doi.org/10.26650/ijmath.2024.00018 (5 Feb. 2025).


MLA

Basheer, Ayoub, and Thekiso Seretlo. “The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5).” Istanbul Journal of Mathematics, vol. 2, no. 2, 2024, pp. 82-86. [Database Container], https://doi.org/10.26650/ijmath.2024.00018


Vancouver

Basheer A, Seretlo T. The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics [Internet]. 5 Feb. 2025 [cited 5 Feb. 2025];2(2):82-86. Available from: https://doi.org/10.26650/ijmath.2024.00018 doi: 10.26650/ijmath.2024.00018


ISNAD

Basheer, Ayoub - Seretlo, Thekiso. “The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5)”. Istanbul Journal of Mathematics 2/2 (Feb. 2025): 82-86. https://doi.org/10.26650/ijmath.2024.00018



TIMELINE


Submitted09.06.2024
Accepted19.12.2024
Published Online31.12.2024

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