ABSTRACT
Remark 0. For any Abelian group A and any positive number m, define A(m) = {a E A : a™ = e}. Then A(m) < A. (Indeed if am = e and bm = e then (ab~l )rn = am(6m)_1 = ee-1 = e.)
T heorem 2 (Fundamental theorem of finite A belian groups). Every finite Abelian group generated by t elements is isomorphic to a direct product o f t cyclic subgroups.
