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Free 3-Generated Lattices with Two Semi-Normal Generators



We consider a lattice generated by three elements, two of which are semi-normal. We have proved it is infinite and have also found an additional condition for the lattice to be modular. As a result, it is proved that the sublattice generated in the subgroup lattice by two normal subgroups and any subgroup is modular.


Lattice Semi-normal element Defining relation Finite lattice Free lattice 


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Chair of Algebra and Theoretical Computer ScienceUral Federal UniversityEkaterinburgRussia

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