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→Weaker properties
| [[Stronger than::Abelian group]] || any two elements commute || [[locally cyclic implies abelian]] || [[abelian not implies locally cyclic]] || {{intermediate notions short|abelian group|locally cyclic group}}
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| [[Stronger than::Aut-Group whose automorphism group is abelian group]] || automorphism group is abelian || [[locally cyclic implies aut-abelianautomorphism group]] || [[abelian and aut-abelian automorphism group not implies locally cyclic]] || {{intermediate notions short|aut-abelian group|locally cyclic group}}
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| [[Stronger than::Group with at most n elements of order dividing n]] || || || || {{intermediate notions short|group with at most n elements of order dividing n|locally cyclic group}}
