Template:Pivotal group property: Difference between revisions

Latest revision as of 19:15, 3 January 2010

This article defines a group property that is pivotal (i.e., important) among existing group properties
View a list of pivotal group properties | View a complete list of group properties [SHOW MORE]

VIEW RELATED: Group property implications | Group property non-implications | Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions |Group property dissatisfactions<random> @@@
RANDOM GROUP PROPERTY: <random>Simple group: A nontrivial group having no proper nontrivial normal subgroup.@@@Noetherian group: A group where every subgroup is finitely generated.@@@Complete group: A group for which the natural homomorphism to its automorphism group is an isomorphism, i.e., a centerless group for which every automorphism is inner.@@@SQ-universal group: A group for which every finitely generated group can be realized as a subquotient.@@@T-group: A group where any subnormal subgroup is normal, i.e., where normality is transitive. In general, normality is not transitive.@@@Locally finite group: A group in which every finitely generated subgroup is finite.@@@Group satisfying normalizer condition: A group with no proper self-normalizing subgroup.</random></random>

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	{{quotation\|''This article defines a [[group property]] that is pivotal (i.e., important) among existing group properties''<br>[[:Category:Pivotal group properties\|View a list of pivotal group properties]] OR [[:Category:Group properties\|View a complete list of group properties]]'''VIEW RELATED''': {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property implications]]\|limit = 0 \| searchlabel = Group property implications}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property non-implications]]\|limit = 0 \| searchlabel = Group property non-implications}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group metaproperty satisfactions]]\|limit = 0\| searchlabel = Group metaproperty satisfactions}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group metaproperty dissatisfactions]]\|limit = 0\|searchlabel = Group metaproperty dissatisfactions}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property satisfactions]]\|limit = 0\|searchlabel = Group property satisfactions}} <nowiki>\|</nowiki>{{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property dissatisfactions]]\|limit = 0\|searchlabel = Group property dissatisfactions}}<random> @@@<br>{{random group property}}</random>}}<includeonly>[[Category:Pivotal group properties]][[Category:Group properties]]</includeonly><noinclude>[[Category:Property space specification templates]]</noinclude>		{{quotation\|''This article defines a [[group property]] that is pivotal (i.e., important) among existing group properties''<br>[[:Category:Pivotal group properties\|View a list of pivotal group properties]] <nowiki>\|</nowiki> [[:Category:Group properties\|View a complete list of group properties]] <toggledisplay><br>'''VIEW RELATED''': {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property implications]]\|limit = 0 \| searchlabel = Group property implications}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property non-implications]]\|limit = 0 \| searchlabel = Group property non-implications}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group metaproperty satisfactions]]\|limit = 0\| searchlabel = Group metaproperty satisfactions}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group metaproperty dissatisfactions]]\|limit = 0\|searchlabel = Group metaproperty dissatisfactions}} <nowiki>\|</nowiki> {{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property satisfactions]]\|limit = 0\|searchlabel = Group property satisfactions}} <nowiki>\|</nowiki>{{#ask: [[Fact about::{{PAGENAME}}]][[Category:Group property dissatisfactions]]\|limit = 0\|searchlabel = Group property dissatisfactions}}<random> @@@<br>{{random group property}}</random></toggledisplay>}}<includeonly>[[Category:Pivotal group properties]][[Category:Group properties]]</includeonly><noinclude>[[Category:Property space specification templates]]</noinclude>