PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2017 | 9 | 99-110
Tytuł artykułu

Jak bardzo przemienna może być grupa nieprzemienna?

Treść / Zawartość
Warianty tytułu
EN
How abelian can a non-abelian group be?
Języki publikacji
PL
Abstrakty
EN
In this paper we survey, also in historical perspective, the results connected with the notion of the commutativity degree of a finite group, i.e., the probability that two randomly selected elements of the group commute.
Twórcy
Bibliografia
  • Antolín, Y., Martino, A., Ventura, E.: 2017, Degree of commutativity of infinite groups, Proc. Amer. Math. Soc. 145, 479–485.
  • Barry, F., MacHale, D., Ní Shé, Á.: 2006, Some supersolvability conditions for finite groups, Math. Proc. R. Ir. Acad. 106A, 163–177.
  • Baumeister, B., Maróti, A., Tong-Viet, H. P.: 2016, Finite groups have more conjugacy classes, Forum Math. 29, 259–275.
  • Bertram, E. A.: 2013, New reductions and logarithmic lower bounds for the number of conjugacy classes in finite groups, Bull. Austral. Math. Soc. 87, 406–424.
  • Buckley, S. M., MacHale, D.: 2017, Contrasting the commuting probabilities of groups and rings, preprint, http://archive.maths.nuim.ie/staff/sbuckley/Papers/bm_g-vs-r.pdf.
  • Castelaz, A.: 2010, Commutativity degree of finite groups, Master’s thesis, Wake Forest University.
  • Das, A. K., Nath, R. K., Pournaki, M. R.: 2013, A survey on the estimation of commutativity in finite groups, Southeast Asian Bull. Math. 37, 161–180.
  • Dixon, J. D.: 2002, Probabilistic group theory, C. R. Math. Acad. Sci. Soc. R. Can. 24, 1–15.
  • Eberhard, S.: 2015, Commuting probabilities of finite groups, Bull. London Math. Soc. 47, 796–808.
  • Erdös, P., Turán, P.: 1968, On some problems of a statistical group-theory, iv, Acta Math. Acad. Sci. Hung. 19, 413–435.
  • Gallagher, P. X.: 1970, The number of conjugacy classes in a finite group, Math. Z. 118, 175–179.
  • Gallian, J. A.: 2013, Contemporary Abstract Algebra, 8th ed., Belmont, CA, Cengage Learning.
  • Guralnick, R. M., Robinson, G. R.: 2006, On the commuting probability in finite groups, J. Algebra 300, 509–528.
  • Gustafson, W. H.: 1973, What is the probability that two group elements commute?, Amer. Math. Monthly 80, 1031–1034.
  • Hegarty, P.: 2013, Limit points in the range of the commuting probability function on finite groups, J. Group Theory 16, 235–247.
  • Joseph, K. S.: 1969, Commutativity in non-abelian groups, PhD thesis, UCLA.
  • Joseph, K. S.: 1977, Several conjectures on commutativity in algebraic structures, Amer. Math. Monthly 84, 550–551.
  • Landau, E.: 1903, Über die Klassenzahl binären quadratischen Formen von negativer Discriminante, Math. Ann. 56, 671–676.
  • Leavitt, J. L., Sherman, G. J., Walker, M. E.: 1992, Rewriteability in finite groups, Amer. Math. Monthly 99, 446–452.
  • Lescot, P.: 1978, Sur certains groupes finis, Rev. Math. Spéciales, Avril 1987, 276–277.
  • Lescot, P.: 1988, Degré de commutativité et structure d’un groupe fini (1), Rev. Math. Spéciales, Avril 1988, 276–279.
  • MacHale, D.: 1974, How commutative can a non-commutative group be?, Math. Gazette 58, 199–202.
  • MacHale, D.: 1976, Commutativity in finite rings, Amer. Math. Monthly 83, 30–32.
  • MacHale, D.: 1990, Probability in finite semigroups, Irish Math. Soc. Bull. 25, 64–68.
  • Miller, G. A.: 1919, Groups possessing a small number of sets of conjugate operators, Trans. Amer. Math. Soc. 20, 260–270.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-issn-2450-341X-year-2017-volume-9-article-4321
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.