Section 9.5: Analysis

In this final section of Chapter 9 Hungerford discusses the Structure of Finite Groups.  In the previous sections it has been mentioned that groups of order four are isomorphic to or and in this section Hungerford connects this idea to larger groups of prime order or order where p is prime.

Section 9.3: Analysis

This section is mostly about the Sylow Theorems. While these theorems assist in analyzing nonabelian finite groups Hungerford lacks examples in explaining these theorems. The biggest question then is how do the Sylow Theorems help understand nonabelian finite groups?

Section 9.2: Analysis

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 …

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Section 8.4: Analysis

Once again the parallels between groups and rings is shown here. Possibly one of the most interesting parts of this section is the First Isomorphism Theorem. This is an idea that has appeared a few times (as rings and every now and then hints of this have appeared in this section on groups).