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So, the def from
Ballester-Bolinches et al., i.e. Iwasawa=all-subgroups-permutable clearly implies the other/first def, i.e. all subgroups are modular elements in the lattice of subgroups. But does the converse hold? It seems not since B-B et al. only say that "all nilpotent groups with a modular
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The definitions and equivalences in this article need some sorting out... at least in my brain, LOL.
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subgroup lattice are
Iwasawa". So this page seems to operate with two non-equivalent definitions...
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Schmidt defines M-groups as being those that have a modular lattice.
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