Category:Group properties

This is a category of properties for the following kind of objects: groups. In other words, this category lists group properties
View a complete list of property categories

Important group properties, sorted by importance rank:

• Extremely important (importance rank one):

  	Defining ingredient
  Abelian group	Normal subgroup Derived subgroup Center Diagonal-in-square operator
  Cyclic group
  Finite group

• Very important (importance rank two):

  	Defining ingredient
  Finitely presented group	Finitely generated group Presentation of a group
  Nilpotent group	Commutator of two subgroups Subnormal subgroup Center Lower central series Square of a group Commutator Diagonal-in-square operator
  Simple group	Normal subgroup Subnormal subgroup Homomorphism of groups Trivial homomorphism of groups Simple group operator
  Solvable group	Abelian group Normal series Subnormal series Derived series Derived subgroup Characteristic series Fully invariant series

• Somewhat important (importance rank three):

For the full list, including many not-so-important group properties, scroll to the bottom of this page.

Related categories

Related categories include:

• Category:Subgroup properties

Testing/computational problems

• Category:Group property testing problems

Facts and proofs related to group properties

• Category:Group property implications is a page listing implication relations between pairs of group properties, viz describing how/why one group property must imply another.
• Category:Group property non-implications is a page listing non-implication relations between pairs of group properties, viz describing how/why one group property does not imply another.