Kyungpook Mathematical Journal

  • 제56권1호
  • /
  • Pages.121-123
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  • 2016
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  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On a Problem Posed by Belcastro and Sherman

  • 투고 : 2013.08.26
  • 심사 : 2013.10.21
  • 발행 : 2016.03.23
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초록

In this paper, we compute the number of distinct centralizers and commutativity degree of a class of finite groups. These computations produce a further class of examples of groups answering one question raised by Belcastro and Sherman and another one raised by Lescot.

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참고문헌

  1. A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloquium, 7(2)(2000), 139-146. https://doi.org/10.1007/s10011-000-0139-5
  2. A. R. Ashrafi, Counting the centralizers of some finite groups, Korean J. Comput. & Appl. Math, 7(1)(2000), 115-124.
  3. S. M. Belcastro and G. J. Sherman, Counting centralizers in finite groups, Math. Magazine, 67(5)(1994), 366-374. https://doi.org/10.2307/2690998
  4. A. Castelaz, Commutativity degree of finite groups, M. A. thesis, Wake Forest University, (2010) pp: 72-103, pp: 132.
  5. H. Doostie and M. Maghasedi, Certain classes of groups with commutativity degree d(G) < $\frac{1}{2}$, Ars Combinatoria, 89(2008), 263-270.
  6. I. V. Erovenko and B. Sury, Commutativity degree of wreath products of finite abelian groups, Bull. Aus. Math. Soc., 77(1)(2008), 31-36.
  7. P. Lescot, Central extensions and commutativity degree, Comm. Algebra, 29(10)(2001), 4451-4460. https://doi.org/10.1081/AGB-100106768