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## Homework Statement

Consider the group D4 (rigid motions of a square) as a subgroup of S4 by using

permutations of vertices. Identify all the even permutations and show that they form a subgroup of D4.

## The Attempt at a Solution

I think I have the permutations of correct. They are: (1,2,3,4), (1,3)(2,4), (1,4,3,2), (1), (2,4), (1,3), (1,2)(3,4), (1,4)(2,3). If this is correct, then the only one that is not even is (1).

Can someone check my work thus far? I know how to go about proving it is a subgroup assuming the rest is correct.