Question

If σ is an even permutation, then σ² = I .
State the given statement is true or false, give reasons for your answer.

Answer 1

Answer on Question #78775 – Math – Abstract Algebra

Question

If $\sigma$ is an even permutation, then $\sigma^2 = I$.

State the given statement is true or false, give reasons for your answer.

Solution

It is False.

The permutation (123) is even, but (123) squared is equal to (132) and not to an identity permutation.

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