no. 1
Finite Groups with some s-Permutably Embedded and Weakly s-Permutable Subgroups
Xie, Fenfang1 ; Wang, Jinjin1 ; Xia, Jiayi1 ; Zhong, Guo1
1 School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530023, P. R. China
Confluentes Mathematici, Tome 5 (2013) no. 1, pp. 93-101.

Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G with the smallest generator number d. There is a set ℳ d (P)={P 1 ,P 2 ,⋯,P d } of maximal subgroups of P such that ⋂ i=1 d P i =Φ(P). In the present paper, we investigate the structure of a finite group under the assumption that every member of ℳ d (P) is either s-permutably embedded or weakly s-permutable in G to give criteria for a group to be p-supersolvable or p-nilpotent.

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DOI : 10.5802/cml.4
Classification : 20D10, 20D20
Mots clés : weakly $s$-permutable subgoups; $s$-permutably embedded subgroups; $p$-nilpotent groups
Xie, Fenfang 1 ; Wang, Jinjin 1 ; Xia, Jiayi 1 ; Zhong, Guo 1

1 School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi, 530023, P. R. China 
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Xie, Fenfang; Wang, Jinjin; Xia, Jiayi; Zhong, Guo. Finite Groups with some $s$-Permutably Embedded and Weakly $s$-Permutable Subgroups. Confluentes Mathematici, Tome 5 (2013) no. 1, pp. 93-101. doi : 10.5802/cml.4. http://www.numdam.org/articles/10.5802/cml.4/

[1] K. Al-Sharo, On some maximal S-quasinormal subgroups of finite groups, Beiträge zur Algebra und Geometrie, 49:227–232, 2008.

[2] M. Asaad, A. A. Heliel, On S-quasinormal embedded subgroups of finite groups, J. Pure Appl. Algebra, 165:129–135, 2001.

[3] A. Ballester-Bolinches, M. C. Pedraza-Aguilera, Sufficient conditions for supersolubility of finite groups, J. Pure Appl. Algebra, 127:113–118, 1998.

[4] K. Doerk, Finite Soluble Groups, Berlin, Walterde Gruyter, 1992.

[5] W. E. Deskins, On quasinormal subgroups of finite groups, Mathematische Zeitschrift, 82:125–132, 1963.

[6] D. Gorenstein, Finite group, Chelsea, New York, 1980.

[7] B. Huppert, Endliche gruppen I, Springer, Berlin, 1967.

[8] X. He, S. Li, X. Liu, On S-quasinormal and c-normal subgroups of prime power order in finite groups, Algebra Colloq., 18 (2011), 685–692.

[9] O. H. Kegel, Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z., 78:205–221, 1962.

[10] S. Li, X. He, On normally embedded subgroups of prime power order in finite groups, Comm. Algebra, 36:2333–2340, 2008.

[11] S. Li, Y. Li, On S-quasinormal and c-normal subgroups of a finite group, Czechoslovak Mathematical Journal 58:1083–1095, 2008.

[12] S. Li, Z. Shen, J. Liu, et al, The influence of SS-quasinormality of some subgroups on the structure of finite groups, J. Algebra, 319:4275–4287, 2008.

[13] D. H. Mclain, The existence of subgroups of given order in finite groups, Proc.Cambridge Philos.Soc, 53:278–285, 1957.

[14] L. Miao, On weakly s-permutable subgroups of finite groups, Bull Braz. Math. Soc. New Series, 41:223–235, 2010.

[15] D. J. S. Robinson, A course in the Theory of groups, New York, Springer-Verlag, 1982.

[16] Z. Shen, W. Shi, Q. Zhang, S-quasinormality of finite groups, Front. Math. China, 5:329–339, 2010.

[17] P. Schmidt, Subgroups permutable with all Sylow subgroups, J. Algebra, 207:285–293, 1998.

[18] X. Shen, S. Li, W. Shi, Finite groups with normally embedded subgroups, J. Group Theory, 13:257–265, 2010.

[19] A. N. Skiba, On weakly s-permutable subgroups of finite groups, J. Algebra, 315:192–209, 2007.

[20] S. Srinivasan, Two sufficient conditions for supersolvability of finite groups, Israel J.Math, 35:210–214, 1980.

[21] J. G. Thompson, Normal p-complements for finite groups, J. Algebra, 1:43–46, 1964.

[22] Y. Wang, c-normality of groups and its properties, J. Algebra, 180:954–965, 1996.

[23] Y. Wang, Finite groups with some subgroups of Sylow subgroups c-supplemented, J. Algebra, 224:464-478, 2000.

[24] H. Wei, Y. Wang, On c * -normality and its properties, J. Group Theory, 10:211–223, 2007.

[25] H. Wielandt, Subnormal subgroups and permutation groups, lectures given at the Ohio State University, Columbus, Ohio, 1971.

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