7.5, due on 3/16

1.  The only part of the proof of theorem 7.25 that wasn't clear was that "b in G imples b = eb in Kb is a subset of the union of right cosets implies G is a subset of the union of the right cosets."  The red part was unclear.  Is it because b was an arbitrary element of G?  In theorem 7.26 does [G:K] mean the number of distinct cosets?  They explain that in the proof but it seems like they should have explained it before they used it.  If they did I missed it.

2.  The first three results were very straightforward and easy to understand.  Theorem 7.25 was very interesting and the proof was pretty clear.  Apart from the [G:K] part theorem 7.26 was very clear.  I liked the second part of corollary 7.27.