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 su...

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Bibliographic Details
Published in:Order (Dordrecht) 2018-07, Vol.35 (2), p.247-252
Main Authors: Gein, A. G., Shushpanov, M. P.
Format: Article
Language:English
Subjects:
Algebra
Discrete Mathematics
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Subgroups
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Summary: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.
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-017-9429-0