Exam 1

Modern Algebra I, Dave Bayer, February 19, 2008

Name:

[1] (5 pts) [2] (5 pts) [3] (5 pts) [4] (5 pts) [5] (5 pts) [6] (5 pts) TOTAL

Please work only one problem per page, starting with the pages provided. Clearly label your answer. If a

problem continues on a new page, clearly state this fact on both the old and the new pages.

[1] Complete each of the following multiplication tables, so that the resulting table is the multiplication rule

for a group G. In each case, what group do you get?

∗1234

11234

22 1

33 1

44

∗1234

11234

22 1

33

44 1

∗123456

1123456

22315 4

33126 5

44 6 5 2

55 3

665432

[2] For each of the groups found in problem 1, let the group act on itself by right multiplication. Use these

actions to ﬁnd permutation representations for each group.