Difficult: I was doing pretty well with this section until I got to the section on cyclic groups. I did not understand this section of the reading at all. The notation was also kind of confusing to me. I just didn't understand what <a> means. The set of all the powers of "a" confused me because I thought that one of the powers of a should eventually equal the identity. Is this wrong? Or is that only when there is finite order? I just got confused by what cyclic groups really are I guess.
Connections: I like the idea of subgroups though. They seem pretty simple to me, especially after dealing with subrings. The theorems that go with subgroups, at least in the beginning of the section, seem to be pretty simple. The theorems seem pretty straight forward to compute to show whether a subset of a group is a subgroup. These theorems were easy for me to follow so I should be able to use them in the proofs for this section.
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