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Groupprops β

Group in which every retract is a free factor

Definition

A group in which every retract is a free factor is a group with the property that every retract of the group is a free factor of the group, i.e., a factor in an internal free product.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Simple group nontrivial; no proper nontrivial normal subgroup |FULL LIST, MORE INFO
Splitting-simple group nontrivial; no proper nontrivial retract |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Group in which every retract is regular |FULL LIST, MORE INFO