▁Sports ▁Club ▁cr ick eters ▁Category : Place ▁of ▁birth ▁missing ▁( l iving ▁people ) <0x0A> </s> ▁In ▁abstract ▁algebra , ▁an ▁ab elian ▁group ▁ ▁is ▁called ▁finit ely ▁generated ▁if ▁there ▁exist ▁finit ely ▁many ▁elements ▁x 1 , ▁... , ▁xs ▁in ▁G ▁such ▁that ▁every ▁x ▁in ▁G ▁can ▁be ▁written ▁in ▁the ▁form ▁x ▁= ▁n 1 x 1 ▁+ ▁n 2 x 2 ▁+ ▁... ▁+ ▁ns xs ▁with ▁integers ▁n 1 , ▁... , ▁ns . ▁In ▁this ▁case , ▁we ▁say ▁that ▁the ▁set ▁ ▁is ▁a ▁generating ▁set ▁of ▁G ▁or ▁that ▁x 1 , ▁... , ▁xs ▁generate ▁G . ▁ ▁Every ▁finite ▁ab elian ▁group ▁is ▁finit ely ▁generated . ▁The ▁finit ely ▁generated ▁ab elian ▁groups ▁can ▁be ▁completely ▁class ified . ▁ ▁Ex amples ▁ ▁The ▁integers , ▁, ▁are ▁a ▁finit ely ▁generated ▁ab elian ▁group . ▁ ▁The ▁integers ▁mod ulo ▁, ▁, ▁are ▁a ▁finite ▁( h ence ▁finit ely ▁generated ) ▁ab elian ▁group . ▁ ▁Any ▁direct ▁sum ▁of ▁finit ely ▁many ▁finit ely ▁generated ▁ab elian ▁groups ▁is ▁again ▁a ▁finit ely ▁generated ▁ab elian ▁group . ▁ ▁Every ▁lattice ▁forms ▁a ▁finit ely ▁generated ▁free ▁ab elian ▁group . ▁ ▁There ▁are ▁no ▁other ▁examples ▁( up ▁to ▁isomorphism ). ▁In ▁particular , ▁the ▁group ▁ ▁of ▁rational ▁numbers ▁is ▁not ▁finit ely ▁generated : ▁if ▁ ▁are ▁rational ▁numbers , ▁pick ▁a ▁natural ▁number ▁ ▁cop r ime ▁to ▁all ▁the