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Finite groups with seminormal Sylow subgroups

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Abstract

In this paper, we prove the following theorem: Let p be a prime number, P a Sylow p-subgroup of a group G and π = π(G) \ {p}. If P is seminormal in G, then the following statements hold: 1) G is a p-soluble group and P′ ≤ O p (G); 2) l p (G) ≤ 2 and l π (G) ≤ 2; 3) if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.

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References

  1. Su, X. Y.: Seminormal subgroups of finite groups. J. Math. (Wuhan), 8(1), 7–9 (1988)

    Google Scholar 

  2. Kegel, O.: Produkte nilpotenter Gruppen. Arch. Math., 12, 90–93 (1961)

    Article  MATH  Google Scholar 

  3. Guralnick, R. M.: Subgroups of prime power index in a simple group. J. Algebra, 81(2), 304–311 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Podgornaya, V. V.: Seminormal subgroups and supersolublitity of finite groups. Vesti NAN Belarus, Ser. Phys.-Math. Science, 4, 22–25 (2000)

    MathSciNet  Google Scholar 

  5. Wang, P. C.: Some fufficient conditions of supersoluble groups. Acta Mathematica Sinica, Chinese Series, 33, 480–485 (1990)

    MATH  Google Scholar 

  6. Wang, P. C.: Some fufficient conditions for a finite group to be solvable. Acta Mathematica Sinica, Chinese Series, 39(6), 820–824 (1996)

    MathSciNet  Google Scholar 

  7. Zhang, Q. H., Wang, L. F.: The influence of s-semipermutable subgroups on the structure of finite groups. Acta Mathematica Sinica, Chinese Series, 48(1), 81–88 (2005)

    MATH  MathSciNet  Google Scholar 

  8. Guo, W. B.: The Theory of Classes of Groups, Science Press-Kluwer Academic Publishers, Beijing-New York-Dordrecht-Boston-London, 2000

    MATH  Google Scholar 

  9. Huppert, B.: Endliche Gruppen I, Berlin-Heidelberg-New York, Springer, 1967

    MATH  Google Scholar 

  10. Lennox, J. C., Stonehewer, S. E.: Subnormal subgroups of groups, Clarendon Press, Oxford, 1987

    MATH  Google Scholar 

  11. Shemetkov, L. A.: Formations of Finite Groups, Moscow, Nauka, 1978.

    MATH  Google Scholar 

  12. Gaschutz, W.: Lectures of subgroups of Sylow type in finite soluble groups, (Notes on pure Mathematics, No. 11), Canberra, Australian National University, 1979

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, P. R. China

    Wen Bin Guo

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, P. R. China

    Wen Bin Guo

Authors
  1. Wen Bin Guo
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Correspondence to Wen Bin Guo.

Additional information

Research is supported by an NNSF grant of China (Grant #10771180)

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Guo, W.B. Finite groups with seminormal Sylow subgroups. Acta. Math. Sin.-English Ser. 24, 1751–1757 (2008). https://doi.org/10.1007/s10114-008-6563-z

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  • DOI: https://doi.org/10.1007/s10114-008-6563-z

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