In this section Hungerford classifies all Finite Abelian Groups. The first section that may cause some confusion is in Theorem 7.9 where he suddenly calls upon k without previously defining it. It seems that k may be the the number such that (in the multiplicative notation) or (in the additive notation).

The Fundamental Theorem of Finite Abelian Groups seems to be very important but Hungerford doesn't explain, or provide more than one example detailing, what it means.