Title: On <i>s</i>-semipermutable or s-quasinormally Embedded Subgroups of Finite Groups
Abstract: Abstract Suppose that G is a finite group and H is a subgroup of G . H is said to be s -semipermutable in G if HG p = G p H for any Sylow p -subgroup Gp of G with ( p , | H |) = 1; 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 . In every non-cyclic Sylow subgroup P of G we fix 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-semipermutable or s -quasinormally embedded in G . Some recent results are generalized and unified.