TY  - JOUR
T1  - The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5)
AU  - Basheer, Ayoub Basheer Mohammed
AU  - Seretlo, Thekiso
PY  - 2024
DA  - December
Y2  - 2024
DO  - 10.26650/ijmath.2024.00018
JF  - Istanbul Journal of Mathematics
PB  - Istanbul University
WT  - DergiPark
SN  - 2980-3020
SP  - 82
EP  - 86
VL  - 2
IS  - 2
LA  - en
AB  - 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.
KW  - Conjugacy classes
KW  - generation
KW  - 𝑛𝑋-complementary generation
KW  - structure constant
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