Abstract
A subgroup H of a finite group G is E-supplemented in G if there is a subgroup K of G such that G=HK and H∩K≤H eG , where H eG denotes the subgroup of H generated by all those subgroups of H which are S-quasinormally embedded in G. In this paper, we investigate the influence of E-supplemented subgroups on the structure of finite groups.
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Ballester-Bolinches, A., Pedraza-Aguilera, M.C.: Sufficient conditions for supersolubility of finite groups. J. Pure Appl. Algebra 127, 113–118 (1998)
Ballester-Bolinches, A., Wang, Y.: Finite groups with some C-normal minimal subgroups. J. Pure Appl. Algebra 153, 121–127 (2000)
Kegel, O.H.: Sylow-Gruppen und subnormalteiler endlicher Gruppen. Math. Z. 78, 205–221 (1962)
Guo, W.: The Theory of Classes of Groups. Science Press/Kluwer Academic, Dordrecht (2000)
Huang, Y., Li, Y.: On weakly s-supplemented subgroups of finite groups. Southeast Asian Bull. Math. 33, 443–450 (2009)
Huppert, B.: Endliche Gruppen I. Springer, Berlin (1967)
Huppert, B., Blackburn, N.: Finite Groups III. Springer, Berlin (1982)
Li, C.: A note on a result of Skiba. J. Group Theory 15, 385–396 (2012)
Li, Y., Wang, Y.: On π-quasinormally embedded subgroups of finite group. J. Algebra 281, 109–123 (2004)
Li, Y., Wang, Y., Wei, H.: On p-nilpotency of finite groups with some subgroups π-quasinormally embedded. Acta Math. Hung. 108, 283–298 (2005)
Robinson, D.J.S.: A Course in Theory of Group. Springer, Berlin (1982)
Skiba, A.N.: On weakly s-permutable subgroups of finite groups. J. Algebra 315, 192–209 (2007)
Wang, Y.: The influence of minimal subgroups on the structure of finite group. Acta Math. Sin. 16, 63–70 (2000)
Wang, Y., Li, Y., Wang, J.: Finite groups with c-supplemented minimal subgroups. Algebra Colloq. 10, 413–425 (2003)
Acknowledgements
The project is supported by the Natural Science Foundation of China (No: 11101369) and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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Zhang, X., Li, C. Finite Groups with E-Supplemented Subgroups. Viet J Math 41, 333–339 (2013). https://doi.org/10.1007/s10013-013-0021-7
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DOI: https://doi.org/10.1007/s10013-013-0021-7