Free implies every subgroup is descendant
This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., free group) must also satisfy the second group property (i.e., group in which every subgroup is descendant)
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- Free implies residually nilpotent
- Residually nilpotent implies hypocentral
- Hypocentral implies every subgroup is descendant
The proof follows by combining Facts (1)-(3).