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Locally cyclic group

1,219 bytes added, 23:38, 10 January 2010
Relation with other properties
===Stronger properties===
* {| class="sortable" border="1"! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions|-| [[Weaker than::Cyclic group]]|| generated by one element || || [[locally cyclic not implies cyclic]] || {{intermediate notions short|locally cyclic group|cyclic group}}|}
===Weaker properties===
* {| class="sortable" border="1"! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions|-| [[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}}|-* | [[Stronger than::Aut-abelian group]] || automorphism group is abelian || [[locally cyclic implies aut-abelian]] || [[abelian and aut-abelian not implies locally cyclic]] || {{intermediate notions short|aut-abelian group|locally cyclic group}}|-| [[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}}|-| [[Stronger than::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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