7.6 Part 2, due on Friday, March 25

1. The hardest part of this reading for me is why in Theorem 7.34 - the 5 equivalent statements about normal subgroups - are statements #2 and #4 necessary as well as #3 and #5. Why do we need subsets and equal to for aNa-1, as well as with a-1Na. Wouldn't it be sufficient to just have statements 1-3 because 4 and 5 are included in 2 and 3? This is why I am confused and why this is the hardest part of the reading, because I do not see a purpose in this.

2. The most interesting part of this reading is that just because a subgroup N of group G is normal so Na = aN for every a in G does not mean that na=an for every n in N. This is fascinating to me. It is almost like a subgroup is normal is everything in G gets hit from both the left cosets and the right cosets but not necessarily that the things hitting are the same cosets from left and right. This is a really interesting idea to think about and this is what I liked learning the most in this section.