Homework 14, due 11/30/2015
1. Let H be an index 2 (i.e. [G : H] = 2) subgroup of a group G. Show that
H is normal.
2. Artin 7.7.4
3. Artin 7.7.5
4. Artin 7.7.6
5. Artin 7.M.5. Include as a solution to part (a) an explanation of why
HN = {hn : h ∈ H, n ∈ N } is a subgroup. (Recall ‘M’ refers to the
‘Miscellaneous Problems’ at the back of the chapter) Read, but don’t do,
Artin 7.M.6.
6. Artin 7.10.7 (Recall that we saw in our discussion of simple groups that
the commutator subgroup is always normal, i.e. carried to itself by all
inner automorphisms.)
7. Do the (no longer) bonus problem (number 7) from Homework 2.
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