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ON WEAKLY s-PERMUTABLY EMBEDDED SUBGROUPS OF FINITE GROUPS II

  • SHOUHONG QIAO (a1) and YANMING WANG (a2)

Abstract

A subgroup H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G=HT and HTHse. In this note, we study the influence of the weakly s-permutably embedded property of subgroups on the structure of G, and obtain the following theorem. Let ℱ be a saturated formation containing 𝒰, the class of all supersolvable groups, and G a group with E as a normal subgroup of G such that G/E∈ℱ. Suppose that P has a subgroup D such that 1<∣D∣<∣P∣ and all subgroups H of P with order ∣H∣=∣D∣ are s-permutably embedded in G. Also, when p=2 and ∣D∣=2 , we suppose that each cyclic subgroup of P of order four is weakly s-permutably embedded in G. Then G∈ℱ.

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Copyright

Corresponding author

For correspondence; e-mail: stswym@mail.sysu.edu.cn

Footnotes

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Project supported by NSF China 11171353.

Footnotes

References

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Keywords

MSC classification

ON WEAKLY s-PERMUTABLY EMBEDDED SUBGROUPS OF FINITE GROUPS II

  • SHOUHONG QIAO (a1) and YANMING WANG (a2)

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