Template:Intersection-closed: Difference between revisions

Revision as of 13:52, 2 August 2009

Intersection-closedness

This subgroup property is intersection-closed: an arbitrary (nonempty) intersection of subgroups with this property, also has this property.
ABOUT THIS PROPERTY: View variations of this property that are intersection-closed | View variations of this property that are not intersection-closed
ABOUT INTERSECTION-CLOSEDNESS: View all intersection-closed subgroup properties (or, strongly intersection-closed properties) | View all subgroup properties that are not intersection-closed | Read a survey article on proving intersection-closedness | Read a survey article on disproving intersection-closedness

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 ===Intersection-closedness===
-{{quotation|''This [[subgroup property]] is [[satisfies metaproperty::intersection-closed subgroup property|intersection-closed]]: an arbitrary (nonempty) intersection of subgroups with this property, also has this property.''{{#ifeq:{{{1|strongly}}}|<br>''In fact, since the property is also [[satisfies metaproperty::identity-true subgroup property|true for every group as a subgroup of itself]], it is a [[satisfies metaproperty::strongly intersection-closed subgroup property]]''.}}<br>'''VIEW''': {{#ask: [[Variation of:{{PAGENAME}}]][[satisfies metaproperty::intersection-closed subgroup property]]|limit = 0|searchlabel = Variations of this property that are intersection-closed}} <nowiki>|</nowiki> {{#ask: [[Variation of:{{PAGENAME}}]][[dissatisfies metaproperty::intersection-closed subgroup property]]|limit = 0|searchlabel = Variations of this property that are not intersection-closed}}<br>{{#ask: [[Satisfies metaproperty::Intersection-closed subgroup property]]|limit = 0|searchlabel = View all intersection-closed subgroup properties}} <nowiki>|</nowiki> {{#ask: [[Satisfies metaproperty::Strongly intersection-closed subgroup property]]|limit = 0|searchlabel = View all strongly intersection-closed subgroup properties}}}}
+{{quotation|''This [[subgroup property]] is [[satisfies metaproperty::intersection-closed subgroup property|intersection-closed]]: an arbitrary (nonempty) intersection of subgroups with this property, also has this property.''{{#ifeq:{{{1|strongly}}}|<br>''In fact, since the property is also [[satisfies metaproperty::identity-true subgroup property|true for every group as a subgroup of itself]], it is a [[satisfies metaproperty::strongly intersection-closed subgroup property]]''.}}<br>'''ABOUT THIS PROPERTY''': {{#ask: [[Variation of:{{PAGENAME}}]][[satisfies metaproperty::intersection-closed subgroup property]]|limit = 0|searchlabel = View variations of this property that are intersection-closed}} <nowiki>|</nowiki> {{#ask: [[Variation of:{{PAGENAME}}]][[dissatisfies metaproperty::intersection-closed subgroup property]]|limit = 0|searchlabel = View variations of this property that are not intersection-closed}}<br>'''ABOUT INTERSECTION-CLOSEDNESS''': {{#ask: [[Satisfies metaproperty::Intersection-closed subgroup property]]|limit = 0|searchlabel = View all intersection-closed subgroup properties}} {{#ask: [[Satisfies metaproperty::Strongly intersection-closed subgroup property]]|limit = 0|searchlabel = (or, strongly intersection-closed properties)}} <nowiki>|</nowiki> {{#ask: [[Dissatisfies metaproperty::Intersection-closed subgroup property]]|limit = 0|searchlabel = View all subgroup properties that are not intersection-closed}} <nowiki>|</nowiki> [[Proving intersection-closedness|Read a survey article on proving intersection-closedness]] <nowiki>|</nowiki> [[Disproving intersection-closedness|Read a survey article on disproving intersection-closedness]]}}<noinclude>[[Category: Subgroup metaproperty satisfaction templates]]</noinclude>
-<noinclude>[[Category: Subgroup metaproperty satisfaction templates]]</noinclude>