https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Strongly_UL-intersection-closed_subgroup_propertyStrongly UL-intersection-closed subgroup property - Revision history2026-04-05T04:50:41ZRevision history for this page on the wikiMediaWiki 1.41.2https://groupprops.subwiki.org/w/index.php?title=Strongly_UL-intersection-closed_subgroup_property&diff=12995&oldid=prevVipul: New page: {{wikilocal}} {{subgroup metaproperty}} ==Definition== A subgroup property <math>p</math> is termed '''strongly UL-intersection-closed''' if for any group <math>G</math>, any (possibly e...2008-09-17T12:33:28Z<p>New page: {{wikilocal}} {{subgroup metaproperty}} ==Definition== A subgroup property <math>p</math> is termed '''strongly UL-intersection-closed''' if for any group <math>G</math>, any (possibly e...</p>
<p><b>New page</b></p><div>{{wikilocal}}<br />
{{subgroup metaproperty}}<br />
<br />
==Definition==<br />
<br />
A subgroup property <math>p</math> is termed '''strongly UL-intersection-closed''' if for any group <math>G</math>, any (possibly empty) indexing set <math>I</math>, and subgroups <matH>H_i \le K_i \le G, i \in I</math>, such that <math>H_i</math> satisfies property <math>p</math> in <math>K_i</math> for each <math>i \in I</math>, we have:<br />
<br />
<math>\bigcap_{i \in I} H_i</math> satisfies property <math>p</math> in <math>\bigcap_{i \in I} K_i</math>.<br />
<br />
A subgroup property is strongly UL-intersection-closed if and only if it is both [[UL-intersection-closed subgroup property|UL-intersection-closed]] and [[identity-true subgroup property|identity-true]].<br />
<br />
==Relation with other metaproperties==<br />
<br />
===Weaker metaproperties===<br />
<br />
* [[Stronger than::UL-intersection-closed subgroup property]]<br />
* [[Stronger than::Strongly intersection-closed subgroup property]]<br />
* [[Stronger than::Intersection-closed subgroup property]]<br />
* [[Stronger than::Transfer condition]]<br />
* [[Stronger than::Intermediate subgroup condition]]</div>Vipul