WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
On s-Quasinormally Embedded or Weakly s-Permutable Subgroups of Finite Groups
Authors: ,
Abstract: Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is said to be weakly s-permutable in G if there is a subnormal subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that every subgroup H of P with |H| = |D| is either s-quasinormally embedded or weakly s-permutable in G. Some recent results are generalized and unified.
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Keywords: s-quasinormally embedded subgroup, Weakly s-permutable subgroup, Solvable groups, Saturated formation, Finite groups