Geodesic
On question about semi-modularity of lattice of subgroups of finite groups
Čebyševskij sbornik, Tome 25 (2024) no. 5, pp. 254-261 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 semi-modular and the lattice of subgroups of any proper subgroup of $G$ is lower semi-modular.
Keywords: finite group, semi-modular lattice, generalized semi-modular lattice. 
@article{CHEB_2024_25_5_a17,
     author = {I. A. Tsybin and G. N. Titov},
     title = {On question about semi-modularity of lattice of subgroups of finite groups},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {254--261},
     year = {2024},
     volume = {25},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_5_a17/}
}
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I. A. Tsybin; G. N. Titov. On question about semi-modularity of lattice of subgroups of finite groups. Čebyševskij sbornik, Tome 25 (2024) no. 5, pp. 254-261. http://geodesic.mathdoc.fr/item/CHEB_2024_25_5_a17/