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The Commutativity Degree in the Class of Nonabelian Groups of Same Order

Hojjat Rostami
경북대학교 자연과학대학 수학과|2019.06|Kyungpook Mathematical Journal|제59권 제2호|pp. 203-207|DOI 10.5666/KMJ.2019.59.2.203

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참고문헌

키워드

finite groupcommutativity degreenonnilpotent
주제분류수학

초록

The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. In this paper we give a sharp upper bound of commutativity degree of nonabelial groups in terms of their order.

Abstract

The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. In this paper we give a sharp upper bound of commutativity degree of nonabelial groups in terms of their order.

참고문헌 (9)

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  2. S. Dolfi, "Finite groups whose noncentral commuting elements have centralizers of equal size", Bull. Aust. Math. Soc, 82, pp.293~304 (2010)
  3. R. M. Guralnick, "On the commuting probability in finite groups", J. Algebra, 300(2), pp.509~528 (2006)
  4. W. H. Gustafson, "What is the probability that two group elements commute?", Amer. Math. Monthly, 80(9), pp.1031~1034 (1973)
  5. P. Lescot, "Isoclinism classes and commutativity degrees of finite groups", J. Algebra, 177(3), pp.847~869 (1995)
  6. P. Lescot, "Central extensions and commutativity degree", Comm. Algebra, 29(10), pp.4451~4460 (2001)
  7. J. Pakianathan, "Nilpotent numbers", Amer. Math. Monthly, 107(7), pp.631~634 (2000)
  8. D. J. S. Robinson, "A course in the theory of groups" (1996), Springer-Verlag
  9. D. J. Rusin, "What is the probability that two elements of a finite group commute?", Pacific J. Math, 82(1), pp.237~247 (1979)

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