On NR∗ -subgroups of finite groups

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

: Let G be a finite group and let H be a subgroup of G. H is said to be an NR∗ -subgroup of G if there exists a normal subgroup T of G such that G = HT and if whenever K ✁ H and g ∈ G, then Kg ∩ H ∩ T ≤ K . A number of new characterizations of a group G are given, under the assumption that all Sylow subgroups of certain subgroups of G are NR∗ -subgroups.

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[1] Asaad M, Heliel AA, Al-Mosa Al-Shomrani MM. On weakly H-subgroups of finite groups. Comm Algebra 2012; 40: 35403550.
[2] Berkovich Y. Subgroups with the character restriction property and related topics. Houston J Math 1998; 24: 631638.
[3] Bianchi M, Gillio Berta Mauri A, Herzog M, Verardi L. On finite solvable groups in which normality is a transitive relation. J Group Theory 2000; bf 3: 147156.
[4] Doerk K, Hawkes T. Finite Soluble Groups. Berlin: Walter de Gruyter, 1992.
[5] Gorenstein D. Finite Groups. New York: Chelsea Publishing Company, 1968.
[6] Guo W. The Theory of Class of Groups. Beijing-New York-Dordrecht-Boston: Science Press-Kluwer Academic Publishers, 2000.
[7] Huppert B. Endliche Gruppen I. Berlin: Springer-Verlag, 1967.
[8] Tong-Viet HP. Groups with normal restriction property. Arch Math (Basel) 2009; 93: 199203.
[9] Tong-Viet H P. Normal restriction in finite groups. Comm Algebra 2011; 39: 344354.
[10] Wei X, Guo X. On HC -subgroups and the structure of finite groups. Comm Algebra 2012; 40: 32453256.