Abstract
We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.
Similar content being viewed by others
Data availability
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
References
Bannuscher, W., Tiedt, G.: On a theorem of Deaconescu. Rostock. Math. Kolloq. 47, 23–26 (1994)
Barry, F., MacHale, D., N’iShé, Á.: Some supersolvability conditions for finite groups. Math. Proc. R. Ir. Acad. 106A(2), 163–177 (2006)
Barzegar, R., Erfanian, A., Farrokhi D. G, M.: Finite groups with three relative commutativity degrees. Bull. Iran. Math. Soc. 39(2), 271–280 (2013)
Eberhard, S.: Commuting probabilities of finite groups. Bull. Lond. Math. Soc. 47(5), 796–808 (2015)
Erdös, P., Turan, P.: On some problems of a statistical group-theory, IV. Acta Math. Acad. Sci. Hung. 19, 413–435 (1968)
Erfanian, A., Farrokhi D. G, M.: Finite groups with four relative commutativity degrees,. Algebra Colloq. 22(3), 449–458 (2015)
Erfanian, A., Rezaei, R., Lescot, P.: On the relative commutativity degree of a subgroup of a finite group. Commun. Algebra 35(12), 4183–4197 (2007)
Erovenko, I.V., Sury, B.: Commutativity degrees of wreath products of finite abelian groups. Bull. Aust. Math. Soc. 77(1), 31–36 (2008)
Farrokhi D. G, M., Safa, H.: Subgroups with large relative commutativity degree. Quaest. Math. 40(7), 973–979 (2017)
Guralnik, R.M., Robinson, G.R.: On the commuting probability in finite groups. J. Algebra 300, 509–528 (2006)
Gustafson, W.H.: What is the probability that two group elements commute? Am. Math. Mon. 80, 1031–1034 (1973)
Heffernan, R., Machale, D., NíShé, Á.: Restrictions on commutativity ratios in finite groups. Int. J. Group Theory 3(4), 1–12 (2014)
Hegarty, P.: Limit points in the range of the commuting probability function on finite groups. J. Group Theory 16(2), 235–247 (2013)
Lescot, P.: Isoclinism classes and commutativity degrees of finite groups. J. Algebra 177, 847–869 (1995)
Lescot, P., Nguyen, H.N., Yang, Y.: On the commuting probability and supersolvability of finite groups. Monatsh. Math. 174(4), 567–576 (2014)
Robinson, D.J.S.: A Course in the Theory of Groups, 2nd edn. Spring, New York (1996)
Rusin, D.J.: What is the probability that two elements of a finite group commute? Pac. J. Math. 82, 237–247 (1979)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that no funds, grants, or other support was received during the preparation of this manuscript. The author have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Farrokhi D. G., M. Finite Groups with Five Relative Commutativity Degrees. Results Math 77, 56 (2022). https://doi.org/10.1007/s00025-021-01591-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00025-021-01591-3