1) On the example on pg. 253 in the second edition it says that G(2) is the set of elements having orders 2^0, 2^1, 2^2, etc. And then it says that it is the subgroup {0,3,6,9} which seem to be powers of three, not two? I don't understand how those are supposed to be the same. How can we know or prove if something is of maximal order. I know that it says that elements of maximal order always exist in finite p-groups. Is that the only way to know?
2) I would be curious to know how long it takes people to come up with fundamental theorems, or even just theorems in general. The proof is pretty simple for the Fundamental Theorem of Finite Abelian groups, but to even come up with a conjecture is cool. This is probably a silly question, but are people still trying to play with different constraints and situations in order to come up with different theorems in 371?
No comments:
Post a Comment