Test Review, due on November 27

I think some of the most important theorems and topics we have covered are related to homomorphisms and isomorphisms of groups. I feel like it is easiest to interpret groups when we see what they are isomorphic to. Thus theorems that tell us about normal subgroups and give us the ability to use the first, second, or third isomorphism theorems are the most helpful to understanding groups. I could see this test being very similar to the last one which asks us true false questions about whether certain sets are groups, certain types of groups, whether groups have elements of certain order, etc. Then there will be some questions asking for examples of groups that are isomorphic to Zn or ZnxZm and examples of other types of groups. Then there will probably be some large proof problem asking for some use of the First Isomorphism Theorem for groups like the last test had for rings. I think that there will also be some problem asking for a proof about the order of elements in a group and proving what those orders are (so using Lagrange's theorem).

I need to work on a lot for this test. I think I understood a lot of the material but I didn't really internalize it yet. I also need to work on the last couple of sections that we covered. I have the most difficult time with the material regarding Sn groups (like talking about permutations being odd or even and talking about groups An). I would like to go over problems 7 and 8 on the practice exam because I have a difficult time finding subgroups of groups and I am wondering if there is an easier way to do it that to just check a lot of options.