Some bounds for relative autocommutativity degree
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-03-0042Keywords:
Autocommutativity degree, Automorphism groupAbstract
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.Downloads
References
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
Downloads
Published
Issue
Section
License
Copyright (c) 2020 Rajat Kanti Nath, Parama Dutta
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
