On s-semipermutable or s-quasinormally Embedded Subgroups of Finite Groups

Abstract

of some s-quasinormal subgroup of 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-semipermutable or s-quasinormally embedded in G. Some recent results are generalized and unified.