Category:Group properties

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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
Cyclic group
Finite abelian group
Finite cyclic groupGroup of integers modulo n
Finite group
Group of prime order
Symmetric groupPermutation
Very important (importance rank two):
 Defining ingredient
Finite solvable groupFinite group
Solvable group
Polycyclic group
Composition series
Chief series
Finitely generated abelian groupExternal direct product
Finitely presented groupPresentation of a group
Finitely generated group
Free group
Group of nilpotency class twoNilpotency class
Derived subgroup
Inner automorphism group
Abelian group
Group of prime power order
Metabelian groupSolvable group
Derived length
Derived subgroup
Abelian group
Abelian normal subgroup
Abelian-quotient subgroup
Meta operator
Metacyclic groupCyclic normal subgroup
Cyclic group
Simple groupNormal subgroup
Surjective homomorphism of groups
Homomorphism of groups
Trivial homomorphism
Subnormal subgroup
Simple group operator
Solvable groupNormal series
Abelian group
Subnormal series
Derived series
Derived subgroup
Characteristic series
Fully invariant series
Supersolvable group
Somewhat important (importance rank three):
 Defining ingredient
Almost simple group
Ambivalent groupConjugate elements
Real element
Characteristically simple groupCharacteristic subgroup
Characteristic closure
Characteristic core
Simple group operator
Finitely generated nilpotent group
Hopfian group
Monolithic groupMinimal normal subgroup
Normal subgroup
Noetherian groupHereditarily operator
Finitely generated group
Quasisimple group
Rational groupFully normalized subgroup
Rationally powered group
Residually finite groupSubgroup of finite index
Normal subgroup of finite index
Profinite completion of a group
Subdirect product
Direct product of finite groups
Profinite topology
Residually operator
Finite group
SQ-universal groupFinitely generated group
Finitely generated free group
Free group:F2

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

Related categories

Related categories include:

Testing/computational problems

Facts and proofs related to group properties

Pages in category "Group properties"

The following 200 pages are in this category, out of 528 total. The count includes redirect pages that have been included in the category. Redirect pages are shown in italics.

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