Abstract
It is proved that if \(G\) is a (generalized) soluble group of infinite rank in which all proper subgroups of infinite rank are permodular, then the subgroup lattice of \(G\) is permodular. As a consequence of this theorem, we obtain shorter proofs for corresponding known results concerning normal or permutable subgroups of groups of infinite rank.
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Communicated by J. S. Wilson.
The authors are members of GNSAGA (INdAM).
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De Falco, M., de Giovanni, F. & Musella, C. A note on groups of infinite rank with modular subgroup lattice. Monatsh Math 176, 81–86 (2015). https://doi.org/10.1007/s00605-014-0610-x
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DOI: https://doi.org/10.1007/s00605-014-0610-x