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On subgroup functors of finite soluble groups

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Abstract

The principal aim of this paper is to study the regular and transitive subgroup functors in the universe of all finite soluble groups. We prove that they form a complemented and non-modular lattice containing two relevant sublattices. This is the answer to a question (Question 1.2.12) proposed by Skiba (1997) in the finite soluble universe.

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Acknowledgements

This work was supported by the Ministerio de Economía y Competitividad of Spain (Grant No. MTM2014-54707-C3-1-P), National Natural Science Foundation of China (Grant No. 11271085) and the Ministerio de Educación of Spanish Government (Grant No. AP2010-2764).

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Authors and Affiliations

  1. Departament d’Àlgebra, Universitat de València, Burjassot, 46100, Spain

    Adolfo Ballester-Bolinches & Enric Cosme-Llópez

  2. Gomel Branch of International University “MITSO”, Gomel, 246029, Belarus

    Sergey Fedorovich Kamornikov

Authors
  1. Adolfo Ballester-Bolinches
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  2. Enric Cosme-Llópez
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  3. Sergey Fedorovich Kamornikov
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Correspondence to Adolfo Ballester-Bolinches.

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Ballester-Bolinches, A., Cosme-Llópez, E. & Kamornikov, S.F. On subgroup functors of finite soluble groups. Sci. China Math. 60, 439–448 (2017). https://doi.org/10.1007/s11425-015-0330-9

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  • DOI: https://doi.org/10.1007/s11425-015-0330-9

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