Direct product of finite groups

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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

Definition

A group is termed a direct product of finite groups if it is isomorphic to the external direct product of a collection of (possibly infinitely many) finite groups.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite group |FULL LIST, MORE INFO
Direct power of a finite group |FULL LIST, MORE INFO
Direct product of finite groups with only finitely many isomorphism classes of direct factors A direct product of finite groups where there are only finitely many isomorphism classes among the finite groups occurring as the factors in the direct product. |FULL LIST, MORE INFO
Periodic direct product of finite groups A direct product of finite groups that is also a periodic group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Residually finite group A subdirect product of finite groups Profinite group|FULL LIST, MORE INFO