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→Relation with other properties

! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions

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| [[Weaker than::~~Cyclic ~~cyclic group]] || generated by one element || || [[locally cyclic not implies cyclic]] || {{intermediate notions short|locally cyclic group|cyclic group}}

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! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions

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| [[Stronger than::~~Abelian ~~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::~~Group ~~group whose automorphism group is abelian]] || automorphism group is abelian || [[locally cyclic implies abelian automorphism group]] || [[abelian and abelian automorphism group not implies locally cyclic]] || {{intermediate notions short|aut-abelian group|locally cyclic group}}

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| [[Stronger than::~~Group ~~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}}

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| [[Stronger than::~~Group ~~group in which every finite subgroup is cyclic]] || every finite subgroup is cyclic || || || {{intermediate notions short|group in which every finite subgroup is cyclic|locally cyclic group}}

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