On asymptotic commutativity degree of finite groups
Keywords:Finite groups, Commutativity degree
AbstractThe aim of this paper is to give a detailed account of a problema posed by P. Lescot regarding asymptotic commutativity degree of finite groups.
A. Castelaz, "Commutativity degree of finite groups", M. A. thesis, Wake Forest University, 2010. [On line]. Available: https://bit.ly/2N9Vca7
H. Doostie and M. Maghasedi, “Certain classes of groups with commutativity degree d(G) < ”, Ars combinatoria, vol. 89, pp. 263-270, Oct. 2008.
J. Dutta, “On a problem posed by Belcastro and Sherman”, Kyungpook mathematical journal, vol. 56, no. 1, pp. 121—123, 2016. [On line]. Available: https://bit.ly/2VXyp5b
I. Erovenko and B. Sury, “Commutativity degree of wreath products of finite abelian groups”, Bulletin of the australian mathematical society, vol. 77, no. 1, pp. 31-36, Feb. 2008, doi: 10.1017/S0004972708000038
W. Gustafson, “What is the probability that two group elements commute?”, The American mathematical monthly, vol. 80, no. 9, pp. 1031-1034, Nov. 1973, doi: 10.2307/2318778.
P. Lescot, “Isoclinism classes and commutativity degrees of finite groups”, Journal of algebra, vol. 177, no. 3, pp. 847-869, Nov. 1995, doi: 10.1006/jabr.1995.1331.
P. Lescot, “Central extensions and commutativity degree”, Communication in algebra, vol. 29, no. 10, pp. 4451-4460, Mar. 2001, doi: 10.1081/AGB-100106768
R. Nath, “Commutativity degree, its generalizations, and classification of finite groups”, Ph. D. thesis, North-Eastern Hill University, 2010.
R. Nath, “Computing the commutativity degree of a class of finite groups and consequences”, Bulletin of the australian mathematical society, vol. 88, no. 3, pp. 448-452, Dec. 2013, doi: 10.1017/S0004972712001086.
D. Rusin, “What is the probability that two elements of a finite group commute?”, Pacific journal of mathematics, vol. 82, no. 1, pp. 237-247, May 1979, doi: 10.2140/pjm.1979.82.237