MATH 124

Exam 2 Topics

The second exam will focus on material which we've discussed since the first exam.
This includes sections 1.5, 2.1, 2.2, and 2.3 of the textbook.  Of course, earlier
topics (such as group, subgroup, etc.) will show up as well when needed.  Here
is a list of the major things we've studied since the first exam:

Cyclic groups
   They're all isomorphic to Z or Z mod n.
   They're all abelian.
   Subgroups of cyclic groups are cyclic.
You can predict the order of a subgroup of a finite
  cyclic group based on the order of the generator and
  the group (Theorem 1.5.16).
Lattices of subgroups of Z mod n.
Generators of a group.
The intersection of subgroups is a subgroup.
The subgroup generated by a set of generators.
   Viewed as products of the generators.
   Viewed as the intersection of subgroups.
Using a Cayley diagram to find the subgroup generated by
  a set of elements.
Permutation groups.
The Symmetric group, S sub n.
Cayley's Theorem
Orbits
Cycle notation for permutations.
Computing the order of a permutation given in cycle
  notation (the LCM of the cycle lengths).
Even and odd permutations.
the Alternating group, A sub n.
Left and right cosets of a subgroup.
Lagrange's Theorem.
Any prime order group is cyclic.