Abstract
Let G be a finite group and H a subgroup of G. We call that H has IC-property if the intersection of H and [H, G] satisfy some conditions. In this paper, we investigate the structure of finite group G under the assumption that some primary subgroups of G have IC-property and obtain some new results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin-Heidelberg-New York, 1967.
K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin-New York, 1992.
Y. Gao and X. Li, The influence of \(IC\Phi \)-subgroups on the structure of finite groups, Acta Math. Hungar., 163(1), 29-36 (2021)
Y. Fan, X. Guo and K. P. Shum, Remarks on two generalizations of normality of subgroups, Chinese Ann. Math., 27(2006), A no. 2, 169-176.
X. Guo, P. Guo and K. P. Shum, On semi cover-avoiding subgroups of finite groups, J. Pure Appl. Algebra, 209(2007), no. 1, 151-158.
A. Ballester-Bolinches, R. Esteban-Romero and Y. Li, A question on partial \(CAP\)-subgroups of finite groups, Sci. China Math., 55(5), 961-966 (2012)
A. N. Skiba, On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups, J. Group Theory, 13, 841-850 (2010).
W. Guo and A. N. Skiba, On \(\mathfrak{F}\Phi ^*\)-hypercentral subgroups of finite groups, J. Algebra, 372(2012), 275-292.
W. Guo and A. N. Skiba, Finite groups with generalized Ore supplement conditions for primary subgroups, J. Algebra, 432(2015), 205-227.
X. Chen, W. Guo and A. N. Skiba, Some conditions under which a finite group belongs to a Baer-local formatn, Comm. Algebra, 42(2014), 4188-4203.
W. Guo, Structure Theory for Canonical Classes of Finite Groups, Berlin, Springer-Verlag, 2015.
Y. Li, On cover-avoiding subgroups of Sylow subgroups of finite groups, Rend. Semin. Mat. Univ. Padova, 123(2010), 249-258.
B. Huppert, N. Blackburn, Finie Groups III, Springer-Verlag, Berlin-New York, 1982.
Acknowledgements
The authors are grateful to the referee for valuable comments and detailed corrections.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Bakshi Gurmeet Kaur.
This work was supported by the National Natural Science Foundation of China (Grant No. 11871360)
Rights and permissions
About this article
Cite this article
Gao, Y., Li, X. The IC-property of primary subgroups. Indian J Pure Appl Math 54, 110–116 (2023). https://doi.org/10.1007/s13226-022-00235-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-022-00235-8