On self-normalizing subgroups of finite groups

This paper has been published in Journal of Group Theory, 13(1):143-149 (2010). Copyright 2010 by Walter de Gruyter. The final publication is available at www.degruyter.com. http://dx.doi.org/10.1515/jgt.2009.038 http://www.degruyter.com/view/j/jgth.2010.13.issue-1/jgt.2009.038/jgt.2009.038.xml[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively.This research was supported by the grants MTM2004-08219C02-02 and MTM2007-68010-C03-02 from MEC (Spanish Government) and FEDER (European Union) and GV/2007/243 from Generalitat (Valencian Community).http://dx.doi.org/10.1515/jgt.2009.038Ballester Bolinches, A.; Esteban Romero, R.; Li, Y. (2010). On self-normalizing subgroups of finite groups. Journal of Group Theory. 1(13). https://doi.org/10.1515/jgt.2009.038113Agrawal, R. K. (1975). Finite Groups whose Subnormal Subgroups Permute with all Sylow Subgroups. Proceedings of the American Mathematical Society, 47(1), 77. doi:10.2307/2040211Alejandre, M. J., Ballester-Bolinches, A., & Pedraza-Aguilera, M. . (2001). Finite Soluble Groups with Permutable Subnormal Subgroups. Journal of Algebra, 240(2), 705-722. doi:10.1006/jabr.2001.8732Ballester-Bolinches, A., & Esteban-Romero, R. (2001). Sylow permutable subnormal subgroups of finite groups II. Bulletin of the Australian Mathematical Society, 64(3), 479-486. doi:10.1017/s0004972700019948Ballester-Bolinches, A., & Esteban-Romero, R. (2002). Sylow Permutable Subnormal Subgroups of Finite Groups. Journal of Algebra, 251(2), 727-738. doi:10.1006/jabr.2001.9138Beidleman, J. C., Brewster, B., & Robinson, D. J. S. (1999). Criteria for Permutability to Be Transitive in Finite Groups. Journal of Algebra, 222(2), 400-412. doi:10.1006/jabr.1998.7964Beidleman, J. C., Heineken, H., & Ragland, M. F. (2009). Solvable PST-groups, strong Sylow bases and mutually permutable products. Journal of Algebra, 321(7), 2022-2027. doi:10.1016/j.jalgebra.2009.01.007Bryce, R. A., & Cossey, J. (1989). The Wielandt Subgroup of a Finite Soluble Group. Journal of the London Mathematical Society, s2-40(2), 244-256. doi:10.1112/jlms/s2-40.2.244Deskins, W. E. (1963). On quasinormal subgroups of finite groups. Mathematische Zeitschrift, 82(2), 125-132. doi:10.1007/bf01111801Gruppen, in denen das Normalteilersein transitiv ist. (1957). Journal für die reine und angewandte Mathematik (Crelles Journal), 1957(198), 87-92. doi:10.1515/crll.1957.198.87Kegel, O. H. (1962). Sylow-Gruppen und Subnormalteiler endlicher Gruppen. Mathematische Zeitschrift, 78(1), 205-221. doi:10.1007/bf01195169Li, Y. (2006). Finite groups with NE-subgroups. Journal of Group Theory, 9(1). doi:10.1515/jgt.2006.003Ore, O. (1939). Contributions to the theory of groups of finite order. Duke Mathematical Journal, 5(2), 431-460. doi:10.1215/s0012-7094-39-00537-5Robinson, D. J. S. (1968). A Note on Finite Groups in Which Normality is Transitive. Proceedings of the American Mathematical Society, 19(4), 933. doi:10.2307/203534