Abstract
Let G be a group. Then a subgroup A of G is said to be modular in G if (i) \(\langle X, A \cap Z \rangle =\langle X, A \rangle \cap Z\) for all \(X \le G, Z \le G\) such that \(X \le Z\), and (ii) \(\langle A, Y \cap Z \rangle =\langle A, Y \rangle \cap Z\) for all \(Y \le G, Z \le G\) such that \(A \le Z\). We obtain a description of finite groups in which modularity is a transitive relation.
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Research was supported by the National Natural Science Foundation of China (No. 12171126) and Natural Science Foundation of Hainan Province of China (No. 621RC510). Research of the third author was supported by Ministry of Education of the Republic of Belarus (Grant 20211328).
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Liu, AM., Guo, W., Safonova, I.N. et al. Finite groups in which modularity is a transitive relation. Arch. Math. 121, 111–121 (2023). https://doi.org/10.1007/s00013-023-01884-9
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DOI: https://doi.org/10.1007/s00013-023-01884-9