Yıl: 2022 Cilt: 46 Sayı: 1 Sayfa Aralığı: 242 - 256 Metin Dili: İngilizce DOI: 10.3906/mat-2109-64 İndeks Tarihi: 19-07-2022

Commutativity degree of crossed modules

Öz:
In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in GAP and classify crossed modules by using this function.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Alp M, Odabaş A, Uslu EÖ, Wensley CD. Crossed modules and $cat^1-groups$ (manual for the XMod package for GAP), 2019; version 2.77.
  • [2] Alp M, Wensley CD. Enumeration of cat $cat^1-groups$ of low order. International Journal of Algebra and Computation 2000; 10: 407-424.
  • [3] Arvasi Z, Odabaş A. Crossed Modules and $cat^1-groups$ (manual for the XModAlg package for GAP), 2015; version 1.12.
  • [4] Arvasi Z, Odabaş A. Computing 2-dimensional algebras: Crossed modules and $Cat^1-groups$. Journal of Algebra and Its Applications 2016; 15: 165-185.
  • [5] Behrends R, Hammond K, Janjic V, Konovalov A, Linton S, Loidl HW, Maier P, Trinder, P. HPC-GAP: Engineering a 21st-century high-performance computer algebra system, Concurrency and Computation Practice and Experience 2016; 28: 3606-3636.
  • [6] Brown R, Wensley CD. Computation and homotopical applications of induced crossed modules. Journal of Symbolic Computation 2003; 35: 59-72.
  • [7] Brown R, Higgins PJ, Sivera R. non-Abelian algebraic topology. Germany: European Mathematical Society, 2011.
  • [8] Brown R. Higher dimensional group theory: low dimensional topology. London Mathematical Society 1982; 48: 215-238.
  • [9] Brown R. From groups to groupoids: a brief survey. Bulletin of the London Mathematical Society 1987; 19: 113-134.
  • [10] Castelaz A. Commutativity degree of finite groups. Ph.D Thesis, Wake Forest University 2000.
  • [11] Ellis G. Computing group resolutions. Journal of Symbolic Computation 2004; 38: 1077-1118.
  • [12] The GAP Group, GAP – Groups, Algorithms, and Programming, 2019; version 4.10.2.
  • [13] Gallagher PX. The number of conjugacy classes in a finite group. Math. Z. 1970; 118: 130-141.
  • [14] Gustafson WH. What is the probability that two groups elements commute? American Mathematical Monthly 1973; 80: 1031-1034.
  • [15] Huq SA. Commutator, nilpotency and solvability in categories. Quarterly Journal of Mathematics Oxford Series 1968; 19: 363-389.
  • [16] Lescot P. Sur certains groupes finis. Rev. Math. Speciales 1987; 8: 276-277.
  • [17] Lescot P. Isoclinism classes and commutativity degree of finite groups. Journal of Algebra 1995; 177: 847-869.
  • [18] Lescot P, Nguyen HN, Yang Y. On the commutativity probability and supersolvability of fnite groups. Monatshefte für Mathematik 2014; 174: 567-576.
  • [19] Loday J.L. Spaces with finitely many nontrivial homotopy groups. Journal of Pure and Applied Algebra 1982; 24: 179-202.
  • [20] Norrie KJ. Actions and automorphism of crossed modules. Bulletin de la Societe Mathematique de France 1990; 118: 129-146.
  • [21] Norrie KJ. Crossed modules and analogues of group theorems. Ph.D. Thesis, University of London 1987.
  • [22] Porter T. The Crossed Menagerie: an introduction to crossed gadgetry and cohomology in algebra and topology, 2011.
  • [23] Odabaş A, Uslu EÖ, Ilgaz E. Isoclinism of crossed modules. Journal of Symbolic Computation 2016; 74: 408-424.
  • [24] Whitehead JHC. Combinatorial homotopy I-II. Bulletin American Mathematical Society 1949; 55: 213-245, 453-496.
APA Arvasi Z, ILGAZ ÇAĞLAYAN E, Odabas A (2022). Commutativity degree of crossed modules. , 242 - 256. 10.3906/mat-2109-64
Chicago Arvasi Zekeriya,ILGAZ ÇAĞLAYAN ELİF,Odabas Alper Commutativity degree of crossed modules. (2022): 242 - 256. 10.3906/mat-2109-64
MLA Arvasi Zekeriya,ILGAZ ÇAĞLAYAN ELİF,Odabas Alper Commutativity degree of crossed modules. , 2022, ss.242 - 256. 10.3906/mat-2109-64
AMA Arvasi Z,ILGAZ ÇAĞLAYAN E,Odabas A Commutativity degree of crossed modules. . 2022; 242 - 256. 10.3906/mat-2109-64
Vancouver Arvasi Z,ILGAZ ÇAĞLAYAN E,Odabas A Commutativity degree of crossed modules. . 2022; 242 - 256. 10.3906/mat-2109-64
IEEE Arvasi Z,ILGAZ ÇAĞLAYAN E,Odabas A "Commutativity degree of crossed modules." , ss.242 - 256, 2022. 10.3906/mat-2109-64
ISNAD Arvasi, Zekeriya vd. "Commutativity degree of crossed modules". (2022), 242-256. https://doi.org/10.3906/mat-2109-64
APA Arvasi Z, ILGAZ ÇAĞLAYAN E, Odabas A (2022). Commutativity degree of crossed modules. Turkish Journal of Mathematics, 46(1), 242 - 256. 10.3906/mat-2109-64
Chicago Arvasi Zekeriya,ILGAZ ÇAĞLAYAN ELİF,Odabas Alper Commutativity degree of crossed modules. Turkish Journal of Mathematics 46, no.1 (2022): 242 - 256. 10.3906/mat-2109-64
MLA Arvasi Zekeriya,ILGAZ ÇAĞLAYAN ELİF,Odabas Alper Commutativity degree of crossed modules. Turkish Journal of Mathematics, vol.46, no.1, 2022, ss.242 - 256. 10.3906/mat-2109-64
AMA Arvasi Z,ILGAZ ÇAĞLAYAN E,Odabas A Commutativity degree of crossed modules. Turkish Journal of Mathematics. 2022; 46(1): 242 - 256. 10.3906/mat-2109-64
Vancouver Arvasi Z,ILGAZ ÇAĞLAYAN E,Odabas A Commutativity degree of crossed modules. Turkish Journal of Mathematics. 2022; 46(1): 242 - 256. 10.3906/mat-2109-64
IEEE Arvasi Z,ILGAZ ÇAĞLAYAN E,Odabas A "Commutativity degree of crossed modules." Turkish Journal of Mathematics, 46, ss.242 - 256, 2022. 10.3906/mat-2109-64
ISNAD Arvasi, Zekeriya vd. "Commutativity degree of crossed modules". Turkish Journal of Mathematics 46/1 (2022), 242-256. https://doi.org/10.3906/mat-2109-64