Math 8202 Homework 2

Date due: February 8, 2010. There will be a quiz on this day.

Hand in only the starred questions. One of the other problems may show up on the quiz.

If you want me to do in class any of the questions I have given you, do let me know (on or after the due date for the assignment). For instance, if you want me to do on February 8 or later any of the questions below, please tell me.

Section 4.1: 2, 4, 10

A correct wording of Problem 4.1.10(a) is as follows. "Prove that HxK is the union of left cosets xK in an orbit of H acting by left multiplication on the set of left cosets of K."

C. Let G be the group of all isometries (rotations and reflections) of a regular tetrahedron. Show that G is isomorphic to S4. (Hence, G is also isomorphic to the group of rotations of the cube.)

Section 4.2: 2*, 7*, 8*, 9*, 14