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Solved: Use Cayley Table For S4 (see Picture Below) To Com ...
Solved: Use Cayley Table For S4 (see Picture Below) To Com ...

use cayley table for ,s4, (see picture below) to compute the centralizer of (13)(24). please show all work. thank you

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Elements in centralizer of (12)(34) in S4 - The Student Room
Elements in centralizer of (12)(34) in S4 - The Student Room

7/10/2020, · Knowing this I can work out that the order of the centralizer of (12)(34) is 8. So obviously e, (12)(34),(12),(34) are going to be contained within the centralizer. Also, using the hint I can work out Which also tells me is contained within the centralizer. So there are two more elements I would need to find. My answers tell me these are;

Centre of the group S4 - Mathematics Stack Exchange
Centre of the group S4 - Mathematics Stack Exchange

2 Answers2. Let σ ∈ Z ( ,S 4,). Then σ − 1 ( 12) σ = ( 12). But σ − 1 ( 12) σ = ( σ ( 1) σ ( 2)). Hence either σ fixes 1 and 2, or σ flips 1 and 2. Suppose the latter, then σ − 1 ( 123) σ = ( 1 σ ( 3) 2) ≠ ( 123), contradicting the fact that σ is central. So σ fixes 1 and 2.

Centralizer of symmetric group - Mathematics Stack Exchange
Centralizer of symmetric group - Mathematics Stack Exchange

However, lets take a simple case: let's try to find the, centralizer, of $(1,2)(3,4)$ in $S_4$. The answer is $C=\{Id, (1, 2)(3, 4), (1, 2), (3, 4), (1, 3)(2, 4), (1, 4)(2, 3), (1, 4, 2, 3), (1, 3, 2, 4)\}$ .

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how to find the centralizer? | Yahoo Answers
how to find the centralizer? | Yahoo Answers

4/10/2012, · The, centralizer, and, normalizer of S, are subgroups of G, and can provide insight into the structure of G. Then, the, centralizer, of (12)(34) is (34)(12) for all such values belonging to, S4., Good luck!

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