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Lattice characterization of finite nilpotent groups

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Abstract

The paper deals with subnormal and composition subgroups in the framework of weak congruence lattices of groups. Weak congruences of the composition subgroups of a group form a sublattice of the lattice of all weak congruences. We characterize normality and subnormality in purely lattice-theoretic terms. For a finite group G we prove: all subgroups of G are subnormal (i.e., G is nilpotent) if and only if the weak congruence lattice of G is lower semimodular.

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  • 23 July 2021

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Acknowledgements

We are grateful to the anonymous referee for his useful comments.

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Authors and Affiliations

  1. Union University Belgrade, Belgrade, Serbia

    Jelena Jovanović

  2. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000, Serbia

    Branimir Šešelja & Andreja Tepavčević

  3. Mathematical Institute SANU, Kneza Mihaila 36, Belgrade, 11000, Serbia

    Andreja Tepavčević

Authors
  1. Jelena Jovanović
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  2. Branimir Šešelja
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  3. Andreja Tepavčević
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Corresponding author

Correspondence to Andreja Tepavčević.

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Presented by G. Czédli.

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Research is supported by Ministry of Education, Science and Technological Development, through Mathematical Institute of the Serbian Academy of Sciences and Arts in Belgrade and Faculty of Science, University of Novi Sad.

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Jovanović, J., Šešelja, B. & Tepavčević, A. Lattice characterization of finite nilpotent groups. Algebra Univers. 82, 40 (2021). https://doi.org/10.1007/s00012-021-00716-7

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