Geodesic
Characterization of finite groups with some $S$-quasinormal subgroups of fixed order
Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 161-167.

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Let $G$ be a finite group. A subgroup of $G$ is said to be $S$-quasinormal in $G$ if it permutes with every Sylow subgroup of $G$. We fix in every non-cyclic Sylow subgroup $P$ of the generalized Fitting subgroup a subgroup $D$ such that $1 |D| |P|$ and characterize $G$ under the assumption that all subgroups $H$ of $P$ with $|H| = |D|$ are $S$-quasinormal in $G$. Some recent results are generalized.
Keywords: $S$-quasinormality, generalized Fitting subgroup, supersolvability. 
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M. Asaad; Piroska Csörgő. Characterization of finite groups with some $S$-quasinormal subgroups of fixed order. Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 161-167. http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a1/

[1] M. Asaad, P. Csörgő, “The influence of minimal subgroups on the structure of finite groups”, Archiv der Mathematik, 72 (1999), 401–404 | DOI | MR | Zbl

[2] M. Asaad, P. Csörgő, “Characterization of Finite Groups with Some $S$-quasinormal Subgroups”, Monatsh. Math., 146 (2005), 263–266 | DOI | MR | Zbl

[3] M. Asaad, A. A. Heliel, “On $S$-quasinormally embedded subgroups of finite groups”, J. Pure and Applied Algebra, 165 (2001), 129–135 | DOI | MR | Zbl

[4] Junhong Yao, Changqun Wang, Yangming Li, “A note on characterization of finite groups with some $S$-quasinormal subgroups”, Monatsh. Math., 161 (2010), 233–236 | DOI | MR | Zbl

[5] B. Huppert, Endliche Gruppen, v. I, Springer-Verlag, Berlin, 1979

[6] B. Huppert, N. Blackburn, Finite Groups, v. III, Springer-Verlag, Berlin, 1982

[7] O. H. Kegel, “Sylow Gruppen und Subnormalteiler endlicher Gruppen”, Math. Z., 78 (1962), 205–221 | DOI | MR | Zbl

[8] Y. Li, Y. Wang, “The influence of minimal subgroups on the structure of finite groups”, Proc. Amer. Math. Soc., 131 (2003), 337–341 | DOI | MR | Zbl

[9] P. Schmidt, “Subgroups permutable with all Sylow subgroups”, J. Algebra, 267 (1998), 285–293 | DOI | MR

[10] A. N. Skiba, “On weakly $s$-permutable subgroups of finite groups”, J. Algebra, 315 (2007), 192–209 | DOI | MR | Zbl

[11] M. Weinstein (Ed.), Between Nilpotent and Solvable, Polygonal Publishing House, Passaic, 1982 | MR | Zbl