Is there a quick way to determine the equivalence of two group centralizers?

Asked Apr 10 '19 at 19:16

Active Apr 10 '19 at 19:16

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I came across the question asking, for the group G=S4 and Y = to the centralizer of G being (1234), can you find another centralizer of G being equal to Y? The answer was (4321). I am not so sure how to get this without trial and error?

"Let G = S4. The set CG((1234)) = ?"

asked Apr 10 '19 at 19:16

mathguy

See here for a general answer, and here for another example. Then proceed the same way with $(1234)$. – Dietrich Burde Apr 10 '19 at 20:52
The centralizers are equal because $(1,2,3,4)$ is the inverse of $(4,3,2,1)$. – Derek Holt Apr 10 '19 at 21:36

Is there a quick way to determine the equivalence of two group centralizers?

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