Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2024, Cilt: 2 Sayı: 2, 82 - 86, 31.12.2024

Ayoub Basheer Mohammed Basheer , Thekiso Seretlo

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

Öz

Kaynakça

  • A. R. Ashrafi, 2003, nX-complementary generations of the Harada-Norton group HN, Acta Mathematica et Informatica Universitatis Ostraviensis, 11, no. 1, 3-9. google scholar
  • A. R. Ashrafi, 2004, nX-Complementary generations of the sporadic group O0N, Southeast Asian Bulletin of Mathematics, 28, no. 6,1011-1019. google scholar
  • A. R. Ashrafi and G. A. Moghani, 2006, nX-Complementary generations of the Fischer group Fİ23, J. Appl. Math. & Computing, 21, no. 1-2, 393-409. google scholar
  • A. B. M. Basheer and T. T. Seretlo, 2019, On two generation methods for the simple linear group PSL(3,5), Khayyam J. of Math., 5, no. 1, 125-139. google scholar
  • A. B. M. Basheer, M. J. Motalane and T. T. Seretlo, 2021 The (p, q, r)-generations of the alternating group A11, Khayyam J. of Math., 7, no. 2, 165-186. google scholar
  • A. B. M. Basheer and T. T. Seretlo, 2021, The (p, q, r)-generations of the Matheiu group M 22, Southeast Asian Bulletin of Mathematics, 45, no. 1, 11-28. google scholar
  • A. B. M. Basheer and T. T. Seretlo, 2020, The (p, q, r) -generations of the alternating group A10, Quaestiones Mathematicae, 43, no. 3, 395-408. google scholar
  • A. B. M. Basheer, M. J. Motalane, M. G. Sehoana and T. T. Seretlo, 2024 The nX-complem-entary generations of the classes of the Chevalley group G2(3), Mathematics Interdisciplinary Research, 9 no. 4, 443-460. google scholar
  • J. H. Conway et al., 1985, Atlas of Finite Groups, Clarendon Press, Oxford. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G.A. Moghani, 2001, (p, q, r)-generations of the Conway group C01, for odd p, Kumamoto J. Math., 14, 1 - 20. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G. A. Moghani, 2003, (p, q, r)-generations and nX-complementary generations of the sporadic group Ly, Kumamoto J. Math., 16, 13-25. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G. A. Moghani, 2004, nX-complementary generations of the sporadic group C01 , Acta Mathematica Vietnamica, 29, no. 1, 57-75. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G. A. Moghani,2001, (p, q, r) -generations of the sporadic group O’N, London Mathematical Society Lecture Note Series, Groups St. Andrews in Oxford, Cambridge University Press, 304, 101 - 109. google scholar
  • S. Ganief, 1997, 2-Generations of the Sporadic Simple Groups, PhD Thesis, University of Natal, South Africa. google scholar
  • S. Ganief and J. Moori, 1997, 2-generations of the smallest Fischer group Fİ22 , Nova J. Math. Game Theory Algebra 6, no. 2-3, 127-145. google scholar
  • S. Ganeif and J. Moori, 1997, (p, q, r) -generations and nX-complementary generations of the sporadic groups HS and McL., J. Algebra, 188, no. 2, 531-6. google scholar
  • S. Ganief and J. Moori, 1998, Generating pairs for the Conway groups C02 and C03, J. Group Theory, 1, no. 3, 237-256. google scholar
  • S. Ganief and J. Moori, 1999, 2-generations of the fourth Janko group J4 , J. Algebra, 212, no. 3, 305-322. google scholar
  • The GAP Group, 2018, GAP - Groups, Algorithms, and Programming, Version 4.9.3; (http://www.gap-system.org) google scholar
  • A. J. Woldar, 1994, 2-Generation of the sporadic simple groups, Comm. Algebra 22, no. 2, 675-685. google scholar

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

Yıl 2024, Cilt: 2 Sayı: 2, 82 - 86, 31.12.2024

Ayoub Basheer Mohammed Basheer , Thekiso Seretlo

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

Öz

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.

Anahtar Kelimeler

Conjugacy classes generation 𝑛𝑋-complementary generation structure constant

Kaynakça

  • A. R. Ashrafi, 2003, nX-complementary generations of the Harada-Norton group HN, Acta Mathematica et Informatica Universitatis Ostraviensis, 11, no. 1, 3-9. google scholar
  • A. R. Ashrafi, 2004, nX-Complementary generations of the sporadic group O0N, Southeast Asian Bulletin of Mathematics, 28, no. 6,1011-1019. google scholar
  • A. R. Ashrafi and G. A. Moghani, 2006, nX-Complementary generations of the Fischer group Fİ23, J. Appl. Math. & Computing, 21, no. 1-2, 393-409. google scholar
  • A. B. M. Basheer and T. T. Seretlo, 2019, On two generation methods for the simple linear group PSL(3,5), Khayyam J. of Math., 5, no. 1, 125-139. google scholar
  • A. B. M. Basheer, M. J. Motalane and T. T. Seretlo, 2021 The (p, q, r)-generations of the alternating group A11, Khayyam J. of Math., 7, no. 2, 165-186. google scholar
  • A. B. M. Basheer and T. T. Seretlo, 2021, The (p, q, r)-generations of the Matheiu group M 22, Southeast Asian Bulletin of Mathematics, 45, no. 1, 11-28. google scholar
  • A. B. M. Basheer and T. T. Seretlo, 2020, The (p, q, r) -generations of the alternating group A10, Quaestiones Mathematicae, 43, no. 3, 395-408. google scholar
  • A. B. M. Basheer, M. J. Motalane, M. G. Sehoana and T. T. Seretlo, 2024 The nX-complem-entary generations of the classes of the Chevalley group G2(3), Mathematics Interdisciplinary Research, 9 no. 4, 443-460. google scholar
  • J. H. Conway et al., 1985, Atlas of Finite Groups, Clarendon Press, Oxford. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G.A. Moghani, 2001, (p, q, r)-generations of the Conway group C01, for odd p, Kumamoto J. Math., 14, 1 - 20. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G. A. Moghani, 2003, (p, q, r)-generations and nX-complementary generations of the sporadic group Ly, Kumamoto J. Math., 16, 13-25. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G. A. Moghani, 2004, nX-complementary generations of the sporadic group C01 , Acta Mathematica Vietnamica, 29, no. 1, 57-75. google scholar
  • M. R. Darafsheh, A. R. Ashrafi and G. A. Moghani,2001, (p, q, r) -generations of the sporadic group O’N, London Mathematical Society Lecture Note Series, Groups St. Andrews in Oxford, Cambridge University Press, 304, 101 - 109. google scholar
  • S. Ganief, 1997, 2-Generations of the Sporadic Simple Groups, PhD Thesis, University of Natal, South Africa. google scholar
  • S. Ganief and J. Moori, 1997, 2-generations of the smallest Fischer group Fİ22 , Nova J. Math. Game Theory Algebra 6, no. 2-3, 127-145. google scholar
  • S. Ganeif and J. Moori, 1997, (p, q, r) -generations and nX-complementary generations of the sporadic groups HS and McL., J. Algebra, 188, no. 2, 531-6. google scholar
  • S. Ganief and J. Moori, 1998, Generating pairs for the Conway groups C02 and C03, J. Group Theory, 1, no. 3, 237-256. google scholar
  • S. Ganief and J. Moori, 1999, 2-generations of the fourth Janko group J4 , J. Algebra, 212, no. 3, 305-322. google scholar
  • The GAP Group, 2018, GAP - Groups, Algorithms, and Programming, Version 4.9.3; (http://www.gap-system.org) google scholar
  • A. J. Woldar, 1994, 2-Generation of the sporadic simple groups, Comm. Algebra 22, no. 2, 675-685. google scholar
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Araştırma Makalesi
Yazarlar

Ayoub Basheer Mohammed Basheer 0000-0003-3320-4221

Thekiso Seretlo 0000-0003-2834-1942

Yayımlanma Tarihi 31 Aralık 2024
Gönderilme Tarihi 9 Haziran 2024
Kabul Tarihi 19 Aralık 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 2 Sayı: 2

Kaynak Göster

APA Basheer, A. B. M., & 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 ABM, Seretlo T. The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics. Aralık 2024;2(2):82-86. doi:10.26650/ijmath.2024.00018
Chicago Basheer, Ayoub Basheer Mohammed, ve Thekiso Seretlo. “The 𝑛𝑋-Complementary Generations of the Group 𝑃𝑆𝐿(3, 5)”. Istanbul Journal of Mathematics 2, sy. 2 (Aralık 2024): 82-86. https://doi.org/10.26650/ijmath.2024.00018.
EndNote Basheer ABM, Seretlo T (01 Aralık 2024) The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics 2 2 82–86.
IEEE A. B. M. Basheer ve T. Seretlo, “The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5)”, Istanbul Journal of Mathematics, c. 2, sy. 2, ss. 82–86, 2024, doi: 10.26650/ijmath.2024.00018.
ISNAD Basheer, Ayoub Basheer Mohammed - Seretlo, Thekiso. “The 𝑛𝑋-Complementary Generations of the Group 𝑃𝑆𝐿(3, 5)”. Istanbul Journal of Mathematics 2/2 (Aralık 2024), 82-86. https://doi.org/10.26650/ijmath.2024.00018.
JAMA Basheer ABM, Seretlo T. The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics. 2024;2:82–86.
MLA Basheer, Ayoub Basheer Mohammed ve Thekiso Seretlo. “The 𝑛𝑋-Complementary Generations of the Group 𝑃𝑆𝐿(3, 5)”. Istanbul Journal of Mathematics, c. 2, sy. 2, 2024, ss. 82-86, doi:10.26650/ijmath.2024.00018.
Vancouver Basheer ABM, Seretlo T. The 𝑛𝑋-complementary generations of the group 𝑃𝑆𝐿(3, 5). Istanbul Journal of Mathematics. 2024;2(2):82-6.
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