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Journals / Ikonion Journal of Mathematics / 2022 / Volume: 4 Issue: 2

THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS

Elis Soylu Yılmaz(Eskişehir Osmangazi Üniversitesi)
Ummahan Ege Arslan(ESKISEHIR OSMANGAZI UNIVERSITY)
Şahika Kundakçıoğlu(ESKISEHIR OSMANGAZI UNIVERSITY)
Pages
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Publication Date
2022-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

So we have presented a GAP application for ultra-group theory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we introduce a system computational programming of the ultra-group notions with GAP, Groups, Algorithms and Programming.
📊
Key Findings & Data:We have constructed some algorithms about ultra-groups and their substructures with GAP language.
💡
Conclusion & Impact:So we have presented a GAP application for ultra-group theory.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ultra-group · normal ultra-group · GAP programming language

Abstract

In this work, we introduce a system computational programming of the ultra-group notions with GAP, Groups, Algorithms and Programming. We have constructed some algorithms about ultra-groups and their substructures with GAP language. Also, we give the GAP algorithm about ultra-group homomorphism. So we have presented a GAP application for ultra-group theory.

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Cite This Article

Yılmaz, E. S., Arslan, U. E., Kundakçıoğlu, Ş. (2022). THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS. Ikonion Journal of Mathematics, Volume: 4 Issue: 2. https://doi.org/10.54286/ikjm.1136706

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References (16)

  1. Alp, M.,Wensley, C.D. (2015) Crossed Modules and cat1-groups in GAP Version 2.43, Manual for the XMod share package for GAP4, http://www.gap-system.org/Packages/xmod.html.
  2. Besche, H. U., Eick, B. (1999) The groups of order at most 1000 except 512 and 768, Journal of Symbolic Computation, 27 (4): 405-413.
  3. Eick, B. and Nickel, W. (2000) Polycyclic, A GAP 4.
  4. Eick,B., Besche, H. U., O’brien, E. A. (2002) A Millennium Project: Constructing Small Groups, International Journal of Algebra and Computation, 12 (05): 623-644.
  5. Kurosh, A. (1960) The theory of groups, American Mathematical Society.
  6. Moghaddasi, G.H., Tolue, B., Zolfaghari, P. (2016) On the structure of ultra-groups over a finite group, U.P.B. Sci. Bull. Series A, 78(2): 173-184.
  7. Moghaddasi, G.H., Zolfaghari, P. (2016) The quotient ultra-groups, Italian journal of pure and applied mathematics, 36: 211-218.
  8. O’Brien, E. A. (1991) The groups of order 256, Journal of algebra, 143 (1): 219-235.
  9. Odabas, A., Soylu Yılmaz, E. (2021) 2-Dimensional Groups with Action: The Category of Crossed Module of Groups with Action, Journal of Algebra and its Applications, Under review.
  10. Odabas, A. (2020) An Algorithm for computing isoclinism families of groups, Comptes Rendus De L Academie Bulgare Des Sciences, 73 (1): 3-12.
  11. The GAP Group, GAP - Groups, Algorithms, and Programming, (2021) version 4.11.1 (https://www.gap-system.org).
  12. Tolue, B., Moghaddasi, G.H., Zolfaghari, P. (2017) On the category of ultra-groups, Hacettepe Journal of Mathematics and Statistics, 46(3):437 - 447.
  13. Tolue, B., Zolfaghari, P. and Moghaddasi,G.H. Free ultra-groups, generators and relations, Algebra and Discrete Mathematics, 28 (2) (2019) 308–316.
  14. Eick,B., Besche, H. U., O’brien, E. A. (2002) A Millennium Project: Constructing Small Groups, International Journal of Algebra and Computation, 12 (05): 623-644.
  15. Odabas, A., Soylu Yılmaz, E. (2021) 2-Dimensional Groups with Action: The Category of Crossed Module of Groups with Action, Journal of Algebra and its Applications, Under review.
  16. Tolue, B., Moghaddasi, G.H., Zolfaghari, P. (2017) On the category of ultra-groups, Hacettepe Journal of Mathematics and Statistics, 46(3):437 - 447.