Some bounds for relative autocommutativity degree




Autocommutativity degree, Automorphism group


We consider the probability that a randomly chosen element of a subgroup of a finite group G is fixed by an automorphism of G. We obtain several bounds for this probability and characterize some finite groups with respect to this probability.

Author Biographies

Rajat Kanti Nath, Tezpur University.

Dept. of Mathematical Sciences.

Parama Dutta, Tezpur University.

Dept. of Mathematical Sciences


H. Arora and R. Karan, “What is the probability an automorphism fixes a group element?”, Communications in algebra, vol. 45, no. 3, pp. 1141–1150, Oct. 2016, doi: 10.1080/00927872.2016.1206346

P. Dutta and R. K. Nath, “On generalized autocommutativity degree of fixnite groups”, Hacettepe journal of mathematics and statistics, vol. 48, no. 4, pp. 472–478, Dec. 2017, doi: 10.15672/hjms.2017.531

A. Erfanian, R. Rezaei, and P. Lescot, “On the relative commutativity degree of a subgroup of a finite group”, Communications in algebra, vol. 35, no. 12, pp. 4183–4197, Nov. 2007, doi: 10.1080/00927870701545044

P. Hall, “The classification of prime-power groups”, Journal für die reine und angewandte Mathematik (Crelles journal), vol. 1940, no. 182, pp. 130–141, Jul. 1940, doi: 10.1515/crll.1940.182.130

P. Hegarty, “The absolute center of a group”, Journal of algebra, vol. 169, no. 3, pp. 929–935, Nov. 1994., doi: 10.1006/jabr.1994.1318

M. R. R. Moghaddam, F. Saeedi, and E. Khamseh, “The probability of an automorphism fixing a subgroup element of a finite group”, Asian-european journal of mathematics, vol. 04, no. 02, pp. 301–308, Jun. 2011, doi: 10.1142/S1793557111000241

M. R. R. Moghaddam, M. J. Sadeghifard and M. Eshrati, "Some properties of autoisoclinism of groups", Fifth International Group Theory Conference, Islamic Azad University, Mashhad, Iran, 13-15 March, 2013

R. K. Nath and A. K. Das, “On a lower bound of commutativity degree”, Rendiconti del circolo matematico di Palermo, vol. 59, no. 1, pp. 137–142, Apr. 2010, doi: 10.1007/s12215-010-0010-6

R. K. Nath and M. K. Yadav, “Some results on relative commutativity degree”, Rendiconti del circolo matematico di Palermo, vol. 64, no. 2, pp. 229–239, Mar. 2015, doi: 10.1007/s12215-015-0194-x

M. R. Rismanchian and Z. Sepehrizadeh, “Autoisoclinism classes and autocommutativity degrees of finite groups”, Hacettepe journal of mathematics and statistics, vol. 44, no. 4, pp. 893–899, 2015, doi: 10.15672/HJMS.2015449442

Z. Sepehrizadeh and M. Rismanchian, “Probability that an autocommutator element of a finite group equals to a fixed element”, Filomat, vol. 31, no. 20, pp. 6241–6246, 2017, doi: 10.2298/FIL1720241S

G. Sherman, “What is the Probability an Automorphism Fixes a Group Element?”, The american mathematical monthly, vol. 82, no. 3, pp. 261–264, Mar. 1975, doi: 10.2307/2319852



How to Cite

R. K. Nath and P. Dutta, “Some bounds for relative autocommutativity degree”, Proyecciones (Antofagasta, On line), vol. 39, no. 3, pp. 679-691, Jun. 2020.