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Year 2022, Volume: 4 Issue: 2, 1 - 11, 31.12.2022

Elis Soylu Yılmaz , Ummahan Ege Arslan , Şahika Kundakçıoğlu

https://doi.org/10.54286/ikjm.1136706

Abstract

References

  • 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.
  • 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.
  • Eick, B. and Nickel, W. (2000) Polycyclic, A GAP 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.
  • Kurosh, A. (1960) The theory of groups, American Mathematical Society.
  • 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.
  • Moghaddasi, G.H., Zolfaghari, P. (2016) The quotient ultra-groups, Italian journal of pure and applied mathematics, 36: 211-218.
  • O’Brien, E. A. (1991) The groups of order 256, Journal of algebra, 143 (1): 219-235.
  • 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.
  • Odabas, A. (2020) An Algorithm for computing isoclinism families of groups, Comptes Rendus De L Academie Bulgare Des Sciences, 73 (1): 3-12.
  • The GAP Group, GAP - Groups, Algorithms, and Programming, (2021) version 4.11.1 (https://www.gap-system.org).
  • Tolue, B., Moghaddasi, G.H., Zolfaghari, P. (2017) On the category of ultra-groups, Hacettepe Journal of Mathematics and Statistics, 46(3) :437 - 447.
  • Tolue, B., Zolfaghari, P. and Moghaddasi,G.H. Free ultra-groups, generators and relations, Algebra and Discrete Mathematics, 28 (2) (2019) 308–316.

THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS

Year 2022, Volume: 4 Issue: 2, 1 - 11, 31.12.2022

Elis Soylu Yılmaz , Ummahan Ege Arslan , Şahika Kundakçıoğlu

https://doi.org/10.54286/ikjm.1136706

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.

Keywords

Ultra-group normal ultra-group GAP programming language

References

  • 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.
  • 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.
  • Eick, B. and Nickel, W. (2000) Polycyclic, A GAP 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.
  • Kurosh, A. (1960) The theory of groups, American Mathematical Society.
  • 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.
  • Moghaddasi, G.H., Zolfaghari, P. (2016) The quotient ultra-groups, Italian journal of pure and applied mathematics, 36: 211-218.
  • O’Brien, E. A. (1991) The groups of order 256, Journal of algebra, 143 (1): 219-235.
  • 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.
  • Odabas, A. (2020) An Algorithm for computing isoclinism families of groups, Comptes Rendus De L Academie Bulgare Des Sciences, 73 (1): 3-12.
  • The GAP Group, GAP - Groups, Algorithms, and Programming, (2021) version 4.11.1 (https://www.gap-system.org).
  • Tolue, B., Moghaddasi, G.H., Zolfaghari, P. (2017) On the category of ultra-groups, Hacettepe Journal of Mathematics and Statistics, 46(3) :437 - 447.
  • Tolue, B., Zolfaghari, P. and Moghaddasi,G.H. Free ultra-groups, generators and relations, Algebra and Discrete Mathematics, 28 (2) (2019) 308–316.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elis Soylu Yılmaz

Ummahan Ege Arslan

Şahika Kundakçıoğlu

Early Pub Date December 31, 2022
Publication Date December 31, 2022
Acceptance Date September 12, 2022
Published in Issue Year 2022 Volume: 4 Issue: 2

Cite

APA Soylu Yılmaz, E., Ege Arslan, U., & Kundakçıoğlu, Ş. (2022). THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS. Ikonion Journal of Mathematics, 4(2), 1-11. https://doi.org/10.54286/ikjm.1136706
AMA Soylu Yılmaz E, Ege Arslan U, Kundakçıoğlu Ş. THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS. ikjm. December 2022;4(2):1-11. doi:10.54286/ikjm.1136706
Chicago Soylu Yılmaz, Elis, Ummahan Ege Arslan, and Şahika Kundakçıoğlu. “THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS”. Ikonion Journal of Mathematics 4, no. 2 (December 2022): 1-11. https://doi.org/10.54286/ikjm.1136706.
EndNote Soylu Yılmaz E, Ege Arslan U, Kundakçıoğlu Ş (December 1, 2022) THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS. Ikonion Journal of Mathematics 4 2 1–11.
IEEE E. Soylu Yılmaz, U. Ege Arslan, and Ş. Kundakçıoğlu, “THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS”, ikjm, vol. 4, no. 2, pp. 1–11, 2022, doi: 10.54286/ikjm.1136706.
ISNAD Soylu Yılmaz, Elis et al. “THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS”. Ikonion Journal of Mathematics 4/2 (December 2022), 1-11. https://doi.org/10.54286/ikjm.1136706.
JAMA Soylu Yılmaz E, Ege Arslan U, Kundakçıoğlu Ş. THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS. ikjm. 2022;4:1–11.
MLA Soylu Yılmaz, Elis et al. “THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS”. Ikonion Journal of Mathematics, vol. 4, no. 2, 2022, pp. 1-11, doi:10.54286/ikjm.1136706.
Vancouver Soylu Yılmaz E, Ege Arslan U, Kundakçıoğlu Ş. THE THEORY OF ULTRA - GROUPS and GAP APPLICATIONS. ikjm. 2022;4(2):1-11.
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