Abstract
A subgroup \(A\) of a finite group \(G\) is said to be \(S\)-permutably embedded in \(G\) if for each prime \(p\) dividing the order of \(A\), every Sylow \(p\)-subgroup of \(A\) is a Sylow \(p\)-subgroup of some \(S\)-permutable subgroup of \(G\). In this paper we determine how the \(S\)-permutable embedding of several families of subgroups of a finite group influences its structure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asaad, M., Heliel, A.A.: On \(S\)-quasinormally embedded subgroups of finite groups. J. Pure Appl. Algebra 165(2), 129–135 (2001). doi: 10.1016/S0022-4049(00)00183-3
Asaad, M., Heliel, A.A., Ezzat Mohamed, M.: Finite groups with some subgroups of prime power order S-quasinormally embedded. Comm. Algebra 32(5), 2019–2027 (2004). doi:10.1081/AGB-120029920
Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, de Gruyter Expositions in Mathematics, vol. 53. Walter de Gruyter, Berlin (2010). doi:10.1515/9783110220612
Ballester-Bolinches, A., Pedraza-Aguilera, M.C.: On minimal subgroups of finite groups. Acta Math. Hungar. 73(4), 335–342 (1996). doi:10.1007/BF00052909
Ballester-Bolinches, A., Pedraza-Aguilera, M.C.: Sufficient conditions for supersolubility of finite groups. J. Pure Appl. Algebra 127(2), 113–118 (1998). doi:10.1016/S0022-4049(96)00172-7
Doerk, K., Hawkes, T.: Finite Soluble Groups, De Gruyter Expositions in Mathematics, vol. 4. Walter de Gruyter, Berlin (1992). doi:10.1515/9783110870138
Ezquerro, L.M.: On subnormally embedded subgroups of finite groups. In: Ballester-Bolinches, A., Elduque, A., Muñoz-Escolano, J.M. (eds.) Proceedings of the “Meeting on Group Theory and Applications on the occasion of Javier Otal’s 60th birthday” (Zaragoza, June 10–11, 2011), Biblioteca de la Revista Matemática Iberoamericana, pp. 127–149. Real Sociedad Matemática Española, Madrid (2012)
Feldman, A.: Properties of subgroups of solvable groups that imply they are normally embedded. Glasg. Math. J. 45(1), 45–52 (2003). doi:10.1017/S0017089502008972
Huppert, B.: Endliche Gruppen I, Grund. Math. Wiss., vol. 134. Springer Verlag, Berlin (1967)
Li, Y.: Finite groups with some S-permutable subgroups. (Submitted)
Li, Y.: Finite groups with some \(S\)-quasinormally embedded subgroups. Comm. Algebra 38(11), 4202–4211 (2010). doi: 10.1080/00927870903366835
Li, Y., Wang, Y.: On \(\pi \)-quasinormally embedded subgroups of finite group. J. Algebra 281, 109–123 (2004). doi: 10.1016/j.jalgebra.2004.06.026
Li, Y.M., Wang, Y.M., Wei, H.Q.: On \(p\)-nilpotency of finite groups with some subgroups \(\pi \)-quasinormally embedded. Acta Math. Hungar. 108(4), 283–298 (2005). doi: 10.1007/s10474-005-0225-8
Skiba, A.N.: On weakly \(s\)-permutable subgroups of finite groups. J. Algebra 315(1), 192–209 (2007). doi: 10.1016/j.jalgebra.2007.04.025
Wei, X., Guo, X.: On finite groups with prime-power order \(S\)-quasinormally embedded subgroups. Monatsh. Math. 162(3), 329–339 (2011). doi: 10.1007/s00605-009-0175-2
Acknowledgments
The first author was supported by the Ministerio de Ciencia e Innovación of Spain (Grant MTM2010-19938-C03-01), and the second author was supported by the National Natural Science Foundation of China (Grant No. 11171353/A010201) and the Natural Science Foundation of Guangdong Province (S2011010004447). Both authors were also supported by Project of NSFC (11271085).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by J. S. Wilson.
Rights and permissions
About this article
Cite this article
Ballester-Bolinches, A., Li, Y. On \(S\)-permutably embedded subgroups of finite groups. Monatsh Math 172, 247–257 (2013). https://doi.org/10.1007/s00605-013-0497-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-013-0497-y