Template:Random property-theoretic category

Category:Subgroup properties: A listing of hundreds of properties that can be evaluated for a group and a subgroup thereof, such as normal subgroup, maximal subgroup, characteristic subgroup. Salient ones are at Category:Pivotal subgroup properties.@@@Category:Group properties: A listing of hundreds of properties that can be evaluated for a group, and are invariant up to isomorphism. Salient ones are at Category:Pivotal group properties.@@@Category:Group property implications: A listing of pages giving the statement and proof of group property implications: one group property implying another. For instance, abelian implies nilpotent.@@@Category:Subgroup property implications: A listing of pages giving the statement and proof of a property implication between subgroup properties. For instance, characteristic implies normal.@@@Category:Subgroup metaproperty satisfactions: A listing of pages proving that a subgroup property is well-behaved in some sense: it satisfies a subgroup metaproperty. For instance, normality is strongly intersection-closed and characteristicity is transitive.