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The definitions and equivalences in this article need some sorting out... at least in my brain, LOL. 86.127.138.67 (talk) 23:48, 7 April 2015 (UTC)
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 subgroup lattice are Iwasawa". So this page seems to operate with two non-equivalent definitions... Some1Redirects4You (talk) 09:45, 30 April 2015 (UTC)
Schmidt defines M-groups as being those that have a modular lattice. Some1Redirects4You (talk) 09:52, 30 April 2015 (UTC)