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On generalized autocommutativity degree of finite groups

Year 2019, Volume: 48 Issue: 2, 472 - 478, 01.04.2019

Abstract

Let $H$  be  a subgroup of a finite group $G$ and Aut$(G)$ be the automorphism group of $G$. In this paper we introduce and study the probability  that the autocommutator of a randomly chosen pair of elements, one from $H$ and the other from Aut$(G)$, is equal to a given element of  $G$.

References

  • H. Arora and R. Karan, What is the probability an automorphism fixes a group ele- ment?, Comm. Algebra 45 (3), 1141-1150, 2017.
  • P. Dutta and R.K. Nath, On relative autocommutativity degree of a subgroup of a finite group, arXiv:1706.05614v1 [math.GR], 2017.
  • P. Dutta and R.K. Nath, Autocommuting probabilty of a finite group, Comm. Algebra 46 (3), 961-969, 2018.
  • P. Hall, The classification of prime power groups, J. Reine Angew. Math. 182, 130-141, 1940.
  • P.V. Hegarty, The absolute centre of a group, J. Algebra 169 (3), 929-935, 1994.
  • C. J. Hillar and D. L. Rhea, Automorphism of finite abelian groups, Amer. Math. Monthly 114 (10), 917-923, 2007.
  • M.R.R. Moghaddam, M.J. Sadeghifard and M. Eshrati, Some properties of autoisoclin- ism of groups, Fifth International group theory conference, Islamic Azad University, Mashhad, Iran, 13-15 March 2013.
  • M.R.R. Moghaddam, F. Saeedi and E. Khamseh, The probability of an automorphism fixing a subgroup element of a finite group, Asian-Eur. J. Math. 4 (2), 301308, 2011.
  • M.R. Rismanchian and Z. Sepehrizadeh, Autoisoclinism classes and autocommutativity degrees of finite groups, Hacet. J. Math. Stat. 44 (4), 893-899, 2015.
  • G.J. Sherman, What is the probability an automorphism fixes a group element?, Amer. Math. Monthly 82, 261-264, 1975.
Year 2019, Volume: 48 Issue: 2, 472 - 478, 01.04.2019

Abstract

References

  • H. Arora and R. Karan, What is the probability an automorphism fixes a group ele- ment?, Comm. Algebra 45 (3), 1141-1150, 2017.
  • P. Dutta and R.K. Nath, On relative autocommutativity degree of a subgroup of a finite group, arXiv:1706.05614v1 [math.GR], 2017.
  • P. Dutta and R.K. Nath, Autocommuting probabilty of a finite group, Comm. Algebra 46 (3), 961-969, 2018.
  • P. Hall, The classification of prime power groups, J. Reine Angew. Math. 182, 130-141, 1940.
  • P.V. Hegarty, The absolute centre of a group, J. Algebra 169 (3), 929-935, 1994.
  • C. J. Hillar and D. L. Rhea, Automorphism of finite abelian groups, Amer. Math. Monthly 114 (10), 917-923, 2007.
  • M.R.R. Moghaddam, M.J. Sadeghifard and M. Eshrati, Some properties of autoisoclin- ism of groups, Fifth International group theory conference, Islamic Azad University, Mashhad, Iran, 13-15 March 2013.
  • M.R.R. Moghaddam, F. Saeedi and E. Khamseh, The probability of an automorphism fixing a subgroup element of a finite group, Asian-Eur. J. Math. 4 (2), 301308, 2011.
  • M.R. Rismanchian and Z. Sepehrizadeh, Autoisoclinism classes and autocommutativity degrees of finite groups, Hacet. J. Math. Stat. 44 (4), 893-899, 2015.
  • G.J. Sherman, What is the probability an automorphism fixes a group element?, Amer. Math. Monthly 82, 261-264, 1975.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Parama Dutta This is me 0000-0002-6984-9817

Rajat Kanti Nath 0000-0003-4766-6523

Publication Date April 1, 2019
Published in Issue Year 2019 Volume: 48 Issue: 2

Cite

APA Dutta, P., & Kanti Nath, R. (2019). On generalized autocommutativity degree of finite groups. Hacettepe Journal of Mathematics and Statistics, 48(2), 472-478.
AMA Dutta P, Kanti Nath R. On generalized autocommutativity degree of finite groups. Hacettepe Journal of Mathematics and Statistics. April 2019;48(2):472-478.
Chicago Dutta, Parama, and Rajat Kanti Nath. “On Generalized Autocommutativity Degree of Finite Groups”. Hacettepe Journal of Mathematics and Statistics 48, no. 2 (April 2019): 472-78.
EndNote Dutta P, Kanti Nath R (April 1, 2019) On generalized autocommutativity degree of finite groups. Hacettepe Journal of Mathematics and Statistics 48 2 472–478.
IEEE P. Dutta and R. Kanti Nath, “On generalized autocommutativity degree of finite groups”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, pp. 472–478, 2019.
ISNAD Dutta, Parama - Kanti Nath, Rajat. “On Generalized Autocommutativity Degree of Finite Groups”. Hacettepe Journal of Mathematics and Statistics 48/2 (April 2019), 472-478.
JAMA Dutta P, Kanti Nath R. On generalized autocommutativity degree of finite groups. Hacettepe Journal of Mathematics and Statistics. 2019;48:472–478.
MLA Dutta, Parama and Rajat Kanti Nath. “On Generalized Autocommutativity Degree of Finite Groups”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, 2019, pp. 472-8.
Vancouver Dutta P, Kanti Nath R. On generalized autocommutativity degree of finite groups. Hacettepe Journal of Mathematics and Statistics. 2019;48(2):472-8.