CIA-group

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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

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.

External links