On Ss-quasinormal and Weakly S-permutable Subgroups of Finite Groups
نویسنده
چکیده
A subgroup H of a group G is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is called 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 ss-quasinormal or weakly s-permutable in G. Some recent results are generalized and unified. 2000 Mathematics Subject Classification: 20D10, 20D20.
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