https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Modular_not_implies_permutable 2026-08-19T18:03:19Z Revision history for this page on the wiki MediaWiki 1.41.2 https://groupprops.subwiki.org/w/index.php?title=Modular_not_implies_permutable&diff=13507&oldid=prev 2008-10-02T13:14:50Z

<p>New page: {{subgroup property non-implication| stronger = modular subgroup| weaker = permutable subgroup}} ==Statement== A <a href="/wiki/Modular_subgroup" title="Modular subgroup">modular subgroup</a> of a <a href="/wiki/Group" title="Group">group</a> need not be [[permutable subgroup|per...</p> <p><b>New page</b></p><div>{{subgroup property non-implication|<br /> stronger = modular subgroup|<br /> weaker = permutable subgroup}}<br /> <br /> ==Statement==<br /> <br /> A [[modular subgroup]] of a [[group]] need not be [[permutable subgroup|permutable]].<br /> <br /> ==Facts used==<br /> <br /> # [[Maximal implies modular]]<br /> <br /> ==Proof==<br /> <br /> By fact (1), it suffices to construct an example of a group with a maximal subgroup that is not permutable. Indeed, in the [[particular example::symmetric group:S3]], the subgroup of order two generated by a transposition is maximal but not permutable.</div>

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