On question about semi-modularity of lattice of subgroups of finite groups
https://doi.org/10.22405/2226-8383-2024-25-5-254-261
Abstract
This article considers finite groups whose lattice of subgroups satisfy certain generalized semi-modularity conditions. The main result is the theorem: the lattice of subgroups of the finite group 𝐺 is 1-lower semi-modular whenever the lattice of subgroups of 𝐺 is upper semimodular and the lattice of subgroups of any proper subgroup of 𝐺 is lower semi-modular.
About the Authors
Igor Andreevich Tsybin
Kuban State University
Russian Federation
Russian Federation
Georgy Nikolaevich Titov
Kuban State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Tsybin I.A., Titov G.N. On question about semi-modularity of lattice of subgroups of finite groups. Chebyshevskii Sbornik. 2024;25(5):254-261. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-5-254-261
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