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How to make group act on a set?

asked 2016-09-10 06:26:03 -0500

sageuser gravatar image

updated 2016-09-11 06:50:27 -0500

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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answered 2016-09-11 21:07:51 -0500

calc314 gravatar image

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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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.

B r u n o gravatar imageB r u n o ( 2016-09-12 12:37:17 -0500 )edit

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

sageuser gravatar imagesageuser ( 2016-09-13 20:20:45 -0500 )edit

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Asked: 2016-09-10 06:26:03 -0500

Seen: 58 times

Last updated: Sep 11 '16