A subgroup H of a group G is said to be s-c-permutably embedded in G if every Sylow subgroup of H is a Sylow subgroup of some s-conditionally permutable subgroup of G. In this paper, some new characterizations for a finite group to be p-supersoluble or p-nilpotent are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups of Sylow subgroups are s-c-permutably embedded. A series of known results are generalized.

Keywords: finite group, s-c-permutably embedded subgroups, 2-maximal subgroups, Sylow subgroup, p-supersoluble group, p-nilpotent group.

Fan Cheng – Department of Mathematics, Xuzhou Normal University, Xuzhou, China

Jianhong Huang – Department of Mathematics, Xuzhou Normal University, Xuzhou; Department of Mathematics, University of Science and Technology of China, China

Wenjuan Niu – Department of Mathematics, Xuzhou Normal University, Xuzhou, China

Lifang Ma – Department of Mathematics, Xuzhou Normal University, Xuzhou, China

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