Group having no free non-abelian subgroup
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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A group having no free non-abelian subgroup is a group satisfying the following equivalent conditions:
- It has no subgroup that is a free non-abelian subgroup.
- It has no subgroup isomorphic to the free group on two generators.
- For fixed , it has no subgroup isomorphic to a free group on generators.
- It has no subgroup isomorphic to a free group on a countably infinite number of generators.