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# How to make group act on a set?

How to make group act on set? For example, the set is s A={1, 2} and the group is SymmetricGroup(3). I would like to calculate the output put each permutation map of elements of Symmetric Group so that I can calculate normaizer and stablizer.

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## 1 Answer

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To compute the group action you want:

G=SymmetricGroup(3)
A={1,2}
for g in G:
for a in A:
print str(g)+' acts on '+str(a)+' to give '+str(g(a))

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## Comments

I am not sure that this computes what the OP wants: you get for instance

(1,3,2) acts on 1 to give 3


while $3$ is not in A.

( 2016-09-12 19:37:17 +0200 )edit

Yes, this is what I exactly want!! I didn't know the group elements could be used as function.

( 2016-09-14 03:20:45 +0200 )edit

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Asked: 2016-09-10 13:26:03 +0200

Seen: 171 times

Last updated: Sep 12 '16