Changes

Jump to: navigation, search

Locally cyclic group

671 bytes removed, 22:48, 1 July 2017
Weaker properties conditional to nontriviality
|-
| [[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}}
|}
 
=== Weaker properties conditional to nontriviality ===
 
The following properties are weaker if we restrict to nontrivial groups.
 
{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Stronger than::splitting-simple group]] || has no proper nontrivial [[complemented normal subgroup]] || || || {{intermediate notions short|splitting-simple group|locally cyclic group}}
|-
| [[Stronger than::directly indecomposable group]] || has no proper nontrivial [[direct factor]] || || || {{intermediate notions short|directly indecomposable group|locally cyclic group}}
|}
Bureaucrats, emailconfirmed, Administrators
38,756
edits

Navigation menu