Finitely generated abelian group
Commutative group where every element is the sum of elements from one finite subset / From Wikipedia, the free encyclopedia
In abstract algebra, an abelian group is called finitely generated if there exist finitely many elements
in
such that every
in
can be written in the form
for some integers
. In this case, we say that the set
is a generating set of
or that
generate
. So, finitely generated abelian groups can be thought of as a generalization of cyclic groups.
Every finite abelian group is finitely generated. The finitely generated abelian groups can be completely classified.