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What are the inverses of the following elements of S4:

 

(a) (1234)

(b) (4321)

(c) (12)(34)

(d) (243)

 Jun 13, 2023
 #1
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(a) (1234): To find its inverse, we need to find a permutation such that when composed with (1234), it returns the identity permutation. We can observe that the inverse of (1234) is (1432), as their composition yields the identity permutation:

(1234) * (1432) = (1)(2)(3)(4) = e,

where e represents the identity permutation.

Therefore, the inverse of (1234) is (1432).

 

(b) (4321): To find its inverse, we need to find a permutation such that when composed with (4321), it returns the identity permutation. We can observe that the inverse of (4321) is (4321) itself since they are the same permutation:

(4321) * (4321) = (4)(3)(2)(1) = e.

Therefore, the inverse of (4321) is (4321).

 Jun 13, 2023
 #2
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Why should we help you? Why are you more important than our own problems? Sorry for bursting your little bubble, but you aren't the center of the universe. Now shut it and wait for your turn.

 Jun 14, 2023

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