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[1] Complete each ofthe following multiplication tables,so that the resulting table isthe multiplication rule
for a group G. In each case, what group do you get?
∗ 1 2 3 4
1 1 2 3 4
2 2 1
3 3 1
4 4
∗ 1 2 3 4
1 1 2 3 4
2 2 1
3 3
4 4 1
∗ 1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 3 1 5 4
3 3 1 2 6 5
4 4 6 5 2
5 5 3
6 6 5 4 3 2
[2] For each of the groups found in problem 1, let the group act on itself by right multiplication. Use these
actionsto find permutation representationsfor each group.
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