http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=Conjugate-permutable_subgroup 2026-05-15T18:19:59Z Revision history for this page on the wiki MediaWiki 1.43.1 http://debianws.lexgopc.com/wiki143/index.php?title=Conjugate-permutable_subgroup&diff=2210515&oldid=prev 2023-08-15T23:17:10Z

<p><a href="https://en.wikipedia.org/wiki/OABOT" class="extiw" title="wikipedia:OABOT">Open access bot</a>: doi updated in citation with #oabot.</p> <p><b>New page</b></p><div>In [[mathematics]], in the field of [[group theory]], a &#039;&#039;&#039;conjugate-permutable subgroup&#039;&#039;&#039; is a [[subgroup]] that commutes with all its [[conjugate subgroup]]s. The term was introduced by [[Tuval Foguel]] in 1997&lt;ref&gt;{{citation<br /> | last = Foguel | first = Tuval<br /> | doi = 10.1006/jabr.1996.6924<br /> | issue = 1<br /> | journal = Journal of Algebra<br /> | mr = 1444498<br /> | pages = 235–239<br /> | title = Conjugate-permutable subgroups<br /> | volume = 191<br /> | year = 1997| doi-access = <br /> }}.&lt;/ref&gt; and arose in the context of the proof that for [[finite group]]s, every [[quasinormal subgroup]] is a [[subnormal subgroup]].<br /> <br /> Clearly, every [[quasinormal subgroup]] is conjugate-permutable.<br /> <br /> In fact, it is true that for a finite group:<br /> <br /> * Every maximal conjugate-permutable subgroup is [[Normal subgroup|normal]].<br /> * Every conjugate-permutable subgroup is a conjugate-permutable subgroup of every intermediate subgroup containing it.<br /> * Combining the above two facts, every conjugate-permutable subgroup is [[Subnormal subgroup|subnormal]].<br /> <br /> Conversely, every 2-subnormal subgroup (that is, a subgroup that is a normal subgroup of a normal subgroup) is conjugate-permutable.<br /> <br /> ==References==<br /> {{reflist}}<br /> <br /> [[Category:Subgroup properties]]</div>

imported>OAbot