CIA-group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
History
Origin
The notion of CIA-group was introduced in a paper titled Groups with a finite covering by isomorphic abelian subgroups authored by Tuval Foguel and Matthew Ragland.
Definition
Symbol-free definition
A group is said to be a CIA-group if it can be expressed as a finite union of isomorphic abelian groups (CIA stands for covered by isomorphism abelian).
Relation with other properties
Stronger properties
- abelian group
- finite Hamiltonian group
Weaker properties
Opposite properties
Metaproperties
Direct products
This group property is direct product-closed, viz., the direct product of an arbitrary (possibly infinite) family of groups each having the property, also has the property
View other direct product-closed group properties
Any direct product of CIA-groups is a CIA-group. The covering abelian groups are in fact simply the direct products of the covering abelian subgroups for the two direct factors.