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ON WEAKLY $S$-PERMUTABLY EMBEDDED SUBGROUPS OF FINITE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  21 July 2016

HAORAN YU
HAORAN YU*
Affiliation:
School of Mathematics, Peking University, Beijing 100871, China email sylowtheorem@pku.edu.cn
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Abstract

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In this paper, we obtain some criteria for $p$-nilpotency and $p$-supersolvability of a finite group and extend some known results concerning weakly $S$-permutably embedded subgroups. In particular, we generalise the main results of Zhang et al. [‘Sylow normalizers and $p$-nilpotence of finite groups’, Comm. Algebra43(3) (2015), 1354–1363].

Keywords

p-nilpotencyp-supersolvabilityweakly S-permutably embedded subgroups

MSC classification

Primary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 437 - 448
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Ballester-Bolinches, A. and Li, Y., ‘On S-permutably embedded subgroups of finite groups’, Monatsh. Math. 172 (2013), 247–257.Google Scholar
Ballester-Bolinches, A. and Pedraza-Aguilera, M. C., ‘Sufficient conditions for supersolubility of finite groups’, J. Pure Appl. Algebra 127 (1998), 113–118.CrossRefGoogle Scholar
Berkovich, Y. and Isaacs, I. M., ‘ p-supersolvability and actions on p-groups stabilizing certain subgroups’, J. Algebra 414 (2014), 82–94.Google Scholar
Chen, X., Guo, W. and Skiba, A. N., ‘Some conditions under which a finite group belongs to a Baer-local formation’, Comm. Algebra 42(10) (2014), 4188–4203.Google Scholar
Deskins, W. E., ‘On quasinormal subgroups of finite groups’, Math. Z. 82 (1963), 125–132.Google Scholar
Gagola, S. M. Jr and Isaacs, I. M., ‘Transfer and Tate’s theorem’, Arch. Math. (Basel) 91 (2008), 300–306.CrossRefGoogle Scholar
Huang, Y., Li, Y. and Qiao, S., ‘On weakly s-permutably embedded subgroups of finite groups (II)’, Front. Math. China 8(4) (2013), 855–867.CrossRefGoogle Scholar
Huppert, B., Endliche Gruppen, Vol. I (Springer, Berlin, 1967).CrossRefGoogle Scholar
Isaacs, I. M., Finite Group Theory (American Mathematical Society, Providence, RI, 2008).Google Scholar
Kegel, O. H., ‘Sylow-Gruppen and Subnormalteiler endlicher Gruppen’, Math. Z. 78 (1962), 205–221.CrossRefGoogle Scholar
Kong, Q., ‘On an extension of the Frobenius’ theorem about p-nilpotency of a finite group’, Monatsh. Math. 175 (2014), 133–138.Google Scholar
Li, C., Huang, J. and Hu, B., ‘A note on p-nilpotency of finite groups’, Monatsh. Math. 179 (2016), 253–258.CrossRefGoogle Scholar
Li, C. and Xie, F., ‘A note on S-quasinormally embedded subgroups’, Monatsh. Math. 176 (2015), 571–573.Google Scholar
Li, C., Yu, X. and Tang, N., ‘Finite p-supersoluble groups with some E–S-supplemented subgroups’, Rend. Semin. Mat. Univ. Padova 133 (2015), 1–10.Google Scholar
Li, C., Zhang, X. and Yi, X., ‘On E–S-supplemented subgroups of finite groups’, Colloq. Math. 131 (2013), 41–51.Google Scholar
Li, Y., Qiao, S. and Wang, Y., ‘On weakly s-permutably embedded subgroups of finite groups’, Comm. Algebra 37(3) (2009), 1086–1097.CrossRefGoogle Scholar
Shen, Z. and Chen, Y., ‘On normally embedded subgroups of a finite group’, J. Algebra Appl. 13(7) 1450028 (2014), 6 pp.Google Scholar
Yu, H., ‘Some sufficient and necessary conditions for p-supersolvablity and p-nilpotence of a finite group’, J. Algebra Appl. 16(1) (2017), 1750052, 9 pp, doi:10.1142/S0219498817500529.CrossRefGoogle Scholar
Zhang, X. and Li, X., ‘A criterion of p-nilpotency of finite groups’, Comm. Algebra 40(10) (2012), 3652–3657.Google Scholar
Zhang, X., Li, X. and Miao, L., ‘Sylow normalizers and p-nilpotence of finite groups’, Comm. Algebra 43(3) (2015), 1354–1363.CrossRefGoogle Scholar