Difficult: For me, I have found that finding and proving groups are isomorphic is rather difficult. I feel like the only way to do this is to create some map, f, and then write out the multiplication/operation tables to show that they are the isomorphic. However, I feel like this could be an insufficient way of proving this, but I have no clue how to show this any other way. So from this section, I still just don't know how to show something is isomorphic with out multiplication tables. And beyond this section, I realized that I am just super confused about cyclic groups and how to know if a group is cyclic and how to find the order of a group as well as its elements. This is probably something I should know, but as I was trying to do the homework for the last section, I found that these concepts were causing me grief.
Connections: I guess the only connections I can make with this section is that the integers modulo a number can be isomorphic to other things, ie rings, groups, etc. So this was something I felt like I understood, however, as I mentioned above, I still find it really hard to find the isomorphic map and how to find if that is indeed a homomorphism. However, I still feel like the definition of an isomorphism is something I have seen before, but I find that I have a harder time showing isomorphisms for groups.
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