HW6, due Monday March 13 (revised date), 2017

  • DF 4.3 #5, #8, #33
  • DF 4.4 #6, #18
  • DF 4.5 #3, #40

Recall that the deadline for completing a bonus problem in Friday March 3.  (It is not necessary to write up the solution.  It is enough to notify the instructor by Friday.  It is not necessary to have a complete solution by that date.)


Exam Feb 22, 2017

The exam will cover up to and including Section 4.2.


The bonus problems (not to be presented during the exam) are as follows:


  • Given the category of finite abelian groups, can you determine which object is which group (up to isomorphism)?
  • Determine the group generated by two adjacent faces of the Rubik’s cube.

HW 4, due Wed Feb 8, 2017

  • DF Section 2.4 #9 #17 (Zorn’s lemma appears in Appendix 1), #18
  • DF Section 3.1 #1, #12.
  • Let F be any field.  Show that there is a 1-1 homormophism from S_n to $GL(n,F)$ given by the action of S_n on the indices i in the standard basis e_1,\ldots,e_n.  Combine this with Cayley’s theorem (page 120) to show that for every finite group G, there exists n, such that G is isomorphic to a subgroup of GL(n,F).
  • Show algebraically that every isometry T of R^2 is a glide reflection provided it has the form $\latex T=T_\lambda A$, where $A\in O(2,R)$, $A\not\in SO(2,R)$, $\latex \lambda\ne 0$.
  • Solve the following problems without submitting a solution
    • DF Section 2.4 #15, #19