Sections 0-11, 13-16, 18, 20 and 36 will be tested on the Final Exam. You
should focus particularly on Sections 8-11, 14-16 and 36. The
last two are perhaps the most important.
The homework problems
assigned, and the Midterms, are a good indicator
of what is going to be on the Final Exam.
I will be expecting you to be able to draw the diagram of subgroups for
some simple enough groups like Dn, for n=3,4,5,6
and Sn or An for n=3 and
4. You should be able to determine which subgroups are normal, and
which are conjugate to each other.
In particular, I may ask you to find Sylow p-subgroups for such
groups, to say how many are they, and what familiar groups are they
isomorphic to.
You may be also asked to find the normalizer of a given subgroup of
such a group.
You should be able to determine the number of conjugacy classes of
permutations of given order in Sn. For example:
find the number of conjugacy classes of permutations of order 6 in
S10.