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Lattice universality of locally finite 2-groups

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Abstract

We prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite 2-group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite 2-group.

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Acknowledgements

The author wishes to thank Alexander Gein, Mikhail Volkov and participants of L. N. Shevrin’s seminar “Algebraic systems” for their comments and useful discussions. Also the author is grateful to the anonymous referees for their kind help in preparing the final version of this paper.

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Authors and Affiliations

  1. Institute of Natural Sciences and Mathematics, Ural Federal University, Mira 19, Yekaterinburg, Russia, 620002

    Vladimir B. Repnitskiǐ

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  1. Vladimir B. Repnitskiǐ
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Correspondence to Vladimir B. Repnitskiǐ.

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Presented by R. Pöschel.

Dedicated to Lev N. Shevrin on his 85th birthday.

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The author was partially supported by the Competitiveness Enhancement Program of Ural Federal University.

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Repnitskiǐ, V.B. Lattice universality of locally finite 2-groups. Algebra Univers. 81, 44 (2020). https://doi.org/10.1007/s00012-020-00672-8

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  • DOI: https://doi.org/10.1007/s00012-020-00672-8

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