Abstract
In 1976 Bioch introduced the concept of n-isoclinism of groups. Using the definition of absolute centre and autocommutator subgroup of a group introduced by Hegarty, the notion of autoisoclinism has been studied in the recent years. In this article we first derive some results from definition of Hegarty. Then we introduce the concept of n-autoisoclinism, and obtain some basic results similar to n-isoclinism.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. C. Bioch, On n-isoclinic groups, Indag. Math. 79 (1976), 400–407.
P. Dutta and R. K. Nath, Autocommuting probability of a finite groups, Comm. Algebra 46 (3) (2018), 961–969.
P. Dutta and R. K. Nath, On generalized autocommutativity degree of finite groups, Hacet. J. Math. Stat. 48 (2) (2019), 472–478.
P. Hall, The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130–141.
P. V. Hegarty, The absolute centre of a group, J. Algebra, 169 (3) (1994), 929–935.
N. S. Hekster, On the structure of \(n\)-isoclinism classes of groups, J. Pure Appl. Algebra, 40 (1984), 63–85.
P. Lescot, Isoclinism classes and commutativity degrees of finite groups, J. Algebra, 177 (1995), 847–869.
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, 2013.
M. R. Rismanchian, \(\nu \)-nilpotent groups and 5-term exact sequence, Comm. Algebra 42 (2014), 1559–1564.
M. R. Rismanchian and Z. Sepehrizadeh, Autoisoclinism classes and autocommutativity degrees of finite groups, Hacet. J. Math. Stat. 44 (4) (2015), 893–899.
Z. Sepehrizadeh and M. R. Rismanchian, Probability that an autocommutator element of a finite group equals to a fixed element, Filomat 31 (20) (2017), 6241–6246.
Z. Sepehrizadeh and M. R. Rismanchian, On the characteristic degree of finite groups, J. Algebraic Systems 6 (1) (2018), 71–80.
Z. Sepehrizadeh and M. R. Rismanchian, Some aspects of (relative) of autonilpotent groups, Iran. J. Sci. Technol. Trans. A Sci. 43 (2019), 2429–2432.
Acknowledgements
The authors are grateful to the referee for useful comments, which improved presentation of the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sepehrizadeh, Z., Rismanchian, M.R. Autocenral series and n-autoisoclinism of groups. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00512-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13226-023-00512-0