Proceedings - Mathematical Sciences

, Volume 126, Issue 1, pp 61–68 | Cite as

The probability that a pair of group elements is autoconjugate

  • MOHAMMAD REZA R MOGHADDAM
  • ESMAT MOTAGHI
  • MOHAMMAD AMIN ROSTAMYARI
Article

Abstract

Let g and h be arbitrary elements of a given finite group G. Then g and h are said to be autoconjugate if there exists some automorphism α of G such that h = gα. In this article, we construct some sharp bounds for the probability that two random elements of G are autoconjugate, denoted by \(\mathcal {P}_{a}(G)\). It is also shown that \(\mathcal {P}_{a}(G)|G|\) depends only on the autoisoclinism class of G.

Keywords

Autoconjugate autoisoclinism autocommutator subgroup autocentre. 

2010 Mathematics Subject Classification.

Primary: 20E45, 20B30 Secondary: 05A05, 05A16. 

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Copyright information

© Indian Academy of Sciences 2016

Authors and Affiliations

  • MOHAMMAD REZA R MOGHADDAM
    • 1
    • 2
  • ESMAT MOTAGHI
    • 2
  • MOHAMMAD AMIN ROSTAMYARI
    • 1
    • 3
  1. 1.Centre of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad and Department of MathematicsKhayyam UniversityMashhadIran
  2. 2.International Campus, Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran
  3. 3.Quchan University of Advanced TechnologyQuchanIran

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