proof that a finite abelian group has element with
If is a finite abelian group, then has an element of order .
Proof. Write . Since is the least common multiple of the orders of each group element, it follows that for each , there is an element whose order is a multiple of , say . Let . Then . The thus have pairwise relatively prime orders, and thus
so that is the desired element.
|Title||proof that a finite abelian group has element with|
|Date of creation||2013-03-22 16:34:05|
|Last modified on||2013-03-22 16:34:05|
|Last modified by||rm50 (10146)|