Alternating Group: Show στσ-1τ-1 ∈ An

Thread starter PhysicsUnderg
Start date Jul 8, 2011
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To show that στσ-1τ-1 belongs to the alternating group An, it is essential to calculate the sign of the element στσ-1τ-1. The sign of a permutation is determined by the number of transpositions in its decomposition. The discussion emphasizes that the product of two permutations and their inverses can be analyzed to determine if the result is an even permutation. Participants suggest focusing on the parity of the permutations involved to conclude that the element indeed lies in An. Understanding the properties of permutation signs is crucial for this proof.

Jul 8, 2011

PhysicsUnderg

For any elements σ, τ ∈ S_n, show that στσ^-1τ^-1 ∈ A_n.

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Jul 8, 2011

micromass

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What did you try already?? Just calculate the sign of the element.

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