On supersolvable saturated fusion systems

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Abstract

In this article the supersolvable fusion systems are introduced and studied. We investigate several classes of groups G whose fusion systems \({{\mathrm{{\mathcal {F}}}}}_{S}(G)\) are supersolvable, where S is a Sylow p-subgroup of G.

Keywords

Saturated fusion system Supersolvable 

Mathematics Subject Classification

20D20 20D15 

Notes

Acknowledgements

This research is supported by the project of NSFC (11401597). The author is very grateful to the referee for his/her corrections to the paper. The author would also like to thank Adolfo Ballester-Bolinches for his help.

References

  1. 1.
    Aschbacher, M., Kessar, R., Oliver, B.: Fusion Systems in Algebra and Topology. Cambridge University Press, Cambridge (2011)CrossRefMATHGoogle Scholar
  2. 2.
    Ballester-Bolinches, A., Ezquerro, L.M., Su, N., Wang, Y.: On the focal subgroup of a saturated fusion system. J. Algebra 468, 72–79 (2016)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Doerk, K., Hawkes, T.: Finite Soluble Groups. Walter de Gruyter & Co., Berlin (1992)CrossRefMATHGoogle Scholar
  4. 4.
    Hall, P.: Complemented groups. J. Lond. Math. Soc. S1–12(2), 201 (1937)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Huppert, B.: Endliche Gruppen I. Springer-Verlag, Berlin (1967)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsSun Yat-sen UniversityGuangzhouChina

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