MATH W4041 Columbia Exam1

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Published on 31 Jan 2019
School
Columbia University
Department
Mathematics
Course
MATH W4041
Professor
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
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[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.
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