How to Prove the Even Permutations in Sn Form a Group?

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To prove that the set of even permutations in Sn, denoted as An, forms a group, one must demonstrate that the elements satisfy the group axioms under permutation composition. The discussion highlights the need for clarity on the group operation involved, which is typically the composition of permutations. Additionally, there is a request for resources or books that can aid in understanding groups and permutations, as the original poster is struggling with the material. The specific elements of A4 were mentioned but not detailed in the discussion. Overall, the focus is on proving the group properties of even permutations while seeking additional learning resources.
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Homework Statement


Prove that the set of even permutations in Sn (i.e, An) is a group.
List the elements of A4


Homework Equations


How do I even try to prove these


The Attempt at a Solution


I have started a new course and am finding the problems very difficult.
Is there any books out there that can help me on groups and permutations.
Any help would be great.
Thanks
 
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You have to show that the elements of the set satisfy the axioms of a group under the group operation (which is not mentioned, but they probably mean combined permutation).
 

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