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ℱƬ-Embedded and ℱƬΦ-Embedded Subgroups of Finite Groups

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Algebra and Logic Aims and scope

Let ℱ be a nonempty formation of groups, Ƭ a subgroup functor, and H a p-subgroup of a finite group G. Suppose also that \( \overline{G}=G/{H}_G \) and \( \overline{H}=H/{H}_G \) . We say that H is ℱƬ -embedded (ℱƬΦ -embedded) in G if, for some quasinormal subgroup \( \overline{T} \) of \( \overline{G} \) and some Ƭ -subgroup \( \overline{S} \) of \( \overline{G} \) contained in \( \overline{H} \) , the subgroup \( \overline{H}\overline{T} \) is S-quasinormal in \( \overline{G} \) and \( \overline{H} \) ∩ \( \overline{T} \) ≤ \( \overline{S} \) Z F(\( \overline{G} \)) (resp., \( \overline{H} \) ∩ \( \overline{T} \) ≤ \( \overline{S} \) Z ℱΦ(\( \overline{G} \))). Using the notions of ℱƬ -embedded and ℱƬ - Φ-embedded subgroups, we give some characterizations of the structure of finite groups. A number of earlier concepts and related results are further developed and unified.

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Authors and Affiliations

  1. University of Science and Technology of China, Hefei, 230026, P. R. China

    X. Chen & W. Guo

  2. F. Skorina Gomel State University, Gomel, 246019, Belarus

    A. N. Skiba

Authors
  1. X. Chen
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  2. W. Guo
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  3. A. N. Skiba
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Corresponding authors

Correspondence to X. Chen, W. Guo or A. N. Skiba.

Additional information

(X. Chen and W. Guo)Supported by an NNSF of China (grant No. 11371335) and by Wu Wen-Tsuu Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences.

(A. N. Skiba) Supported by Chinese Academy of Sciences Visiting Professorship for Senior International Scientists (grant No. 2010T2J12) and by the State Program of Fundamental Research of the Republic of Belarus (grant No. 0112850).

Translated from Algebra i Logika, Vol. 54, No. 3, pp. 351–380, May-June, 2015.

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Chen, X., Guo, W. & Skiba, A.N. ℱƬ-Embedded and ℱƬΦ-Embedded Subgroups of Finite Groups. Algebra Logic 54, 226–244 (2015). https://doi.org/10.1007/s10469-015-9343-8

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  • DOI: https://doi.org/10.1007/s10469-015-9343-8

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