Virtually abelian group: Difference between revisions
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* [[Abelian group]] | * [[Abelian group]] | ||
* [[Locally finite group|locally finite]] [[linear group]] over characteristic zero | * [[Locally finite group|locally finite]] [[linear group]] over characteristic zero | ||
* [[Metacyclic group]] | |||
Revision as of 07:51, 14 February 2012
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of Abelianness|Find other variations of Abelianness |
Definition
Symbol-free definition
A group is said to be virtually Abelian if it has an Abelian subgroup of finite index.
Formalisms
In terms of the virtually operator
This property is obtained by applying the virtually operator to the property: Abelian group
View other properties obtained by applying the virtually operator
Relation with other properties
Stronger properties
- Finite group
- Abelian group
- locally finite linear group over characteristic zero
- Metacyclic group