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	<title>Join-closure operator - Revision history</title>
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	<updated>2026-08-23T07:38:56Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://groupprops.subwiki.org/w/index.php?title=Join-closure_operator&amp;diff=17305&amp;oldid=prev</id>
		<title>Vipul: Created page with &#039;{{subgroup property modifier}}  ==Definition==  The &#039;&#039;&#039;join-closure operator&#039;&#039;&#039; takes a subgroup property &lt;math&gt;p&lt;/math&gt; and outputs the property of being a subgroup that can...&#039;</title>
		<link rel="alternate" type="text/html" href="https://groupprops.subwiki.org/w/index.php?title=Join-closure_operator&amp;diff=17305&amp;oldid=prev"/>
		<updated>2009-03-20T22:30:38Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;#039;{{subgroup property modifier}}  ==Definition==  The &amp;#039;&amp;#039;&amp;#039;join-closure operator&amp;#039;&amp;#039;&amp;#039; takes a &lt;a href=&quot;/wiki/Subgroup_property&quot; title=&quot;Subgroup property&quot;&gt;subgroup property&lt;/a&gt; &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; and outputs the property of being a subgroup that can...&amp;#039;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{subgroup property modifier}}&lt;br /&gt;
&lt;br /&gt;
==Definition==&lt;br /&gt;
&lt;br /&gt;
The &amp;#039;&amp;#039;&amp;#039;join-closure operator&amp;#039;&amp;#039;&amp;#039; takes a [[subgroup property]] &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; and outputs the property of being a subgroup that can be expressed as a [[join of subgroups|join]] of (possibly infinitely many) subgroups, each having property &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; in the whole group.&lt;/div&gt;</summary>
		<author><name>Vipul</name></author>
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