Cyclic implies abelian

From Groupprops
Jump to: navigation, search
This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., cyclic group) must also satisfy the second group property (i.e., abelian group)
View all group property implications | View all group property non-implications
Get more facts about cyclic group|Get more facts about abelian group

Statement

Any cyclic group (i.e., any group generated by only one element) is an abelian group (i.e., any two elements in it commute).

Related facts

Using weaker hypotheses to deduce abelianness

Converse of sorts