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The second question is how do you find the order of the stabilizer of 5 in Sn?

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- Thread starter eddyski3
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- #1

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The second question is how do you find the order of the stabilizer of 5 in Sn?

- #2

Deveno

Science Advisor

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now suppose that σ is in Stab(5). let σ(n) = a (which certainly isn't 5) then (5 n)σ(5 n) takes:

5→n→a→a

n→5→5→n, if a≠n, and

5→n→n→5

n→5→5→n, if a = n.

in either case, we see that (5 n)σ(5 n) is in Stab(n).

thus, the map σ→(5 n)σ(5 n) is an isomorphism of Stab(5) with Stab(n) (it's a bijection because conjugation by any element of a group G is a bijection of G with itself).

but if we have an element of Stab(n), there is a natural isomorphism of this subgroup of S

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