1. The most difficult part of this reading was realizing that because I am still confused on an order of an element, I cannot understand subgroups, especially cyclic subgroups. And the biggest problem is is that I am not sure what it is about a, a^2, a^3,... elements and groups that I do not understand. But I cannot do any of the homework do tomorrow so clearly I do not understand something, and thus, I cannot understand cyclic subgroups and how they work and how to use them, so this is the hardest part of the reading.
2. The most interesting part of this reading was that once again a sub-"something" with only a couple of conditions was introduced. We have subsets, subrings, subfields, etc. and now we have subgroups! It is so interesting how everything in this class connects and parallels to each other. For example, eventually in this section we get to the only conditions for something to be a subgroup is to be a nonempty, finite subset and to be closed under the operation of the group that it is a subset under. Then it is a subgroup! Fascinating!
No comments:
Post a Comment