Template:Join-closed: Difference between revisions
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===Join-closedness=== | ===Join-closedness=== | ||
{{quotation|'''YES''': ''This [[subgroup property]] is [[satisfies metaproperty::join-closed subgroup property|join-closed]]: an arbitrary (nonempty) [[join of subgroups]] with this property, also has this property.''{{#ifeq:{{{1 | {{quotation|'''YES''': ''This [[subgroup property]] is [[satisfies metaproperty::join-closed subgroup property|join-closed]]: an arbitrary (nonempty) [[join of subgroups]] with this property, also has this property.''{{#ifeq:{{{1}}}|strongly|<br>''In fact, since the property is also [[satisfies metaproperty::trivially true subgroup property|true for the trivial subgroup in any group]], it is a [[satisfies metaproperty::strongly join-closed subgroup property]]''.}}<br>'''ABOUT THIS PROPERTY''': {{#ask: [[Variation of::{{PAGENAME}}]][[satisfies metaproperty::join-closed subgroup property]]|limit = 0|searchlabel = View variations of this property that are join-closed}} <nowiki>|</nowiki> {{#ask: [[Variation of::{{PAGENAME}}]][[dissatisfies metaproperty::join-closed subgroup property]]|limit = 0|searchlabel = View variations of this property that are not join-closed}}<br>'''ABOUT JOIN-CLOSEDNESS''': {{#ask: [[Satisfies metaproperty::Join-closed subgroup property]]|limit = 0|searchlabel = View all join-closed subgroup properties}} {{#ask: [[Satisfies metaproperty::Strongly join-closed subgroup property]]|limit = 0|searchlabel = (or, strongly join-closed properties)}} <nowiki>|</nowiki> {{#ask: [[Dissatisfies metaproperty::Join-closed subgroup property]]|limit = 0|searchlabel = View all subgroup properties that are not join-closed}} <nowiki>|</nowiki> [[Proving join-closedness|Read a survey article on proving join-closedness]] <nowiki>|</nowiki> [[Disproving join-closedness|Read a survey article on disproving join-closedness]]}}<noinclude>[[Category: Subgroup metaproperty satisfaction templates]]</noinclude> | ||
Latest revision as of 23:33, 7 August 2009
Join-closedness
YES: This subgroup property is join-closed: an arbitrary (nonempty) join of subgroups with this property, also has this property.
ABOUT THIS PROPERTY: View variations of this property that are join-closed | View variations of this property that are not join-closed
ABOUT JOIN-CLOSEDNESS: View all join-closed subgroup properties (or, strongly join-closed properties) | View all subgroup properties that are not join-closed | Read a survey article on proving join-closedness | Read a survey article on disproving join-closedness