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RESEARCH ARTICLE

Characterization of finite groups with some $S$-quasinormal subgroups of fixed order

M. Asaad^a, Piroska Csörgő<sup>b

a</sup> Cairo University, Faculty of Science, Department of Mathematics, Giza 12613, Egypt
^b Eötvös University, Department of Algebra and Number Theory, Pázmány Péter sétány 1/c, H–1117 Budapest, Hungary

Abstract: 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.

MSC: 20D10, 20D30

Received: 01.02.2012
Revised: 26.05.2012

Language: English

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