Ask Your Question
0

permutation representation

asked 2013-01-27 00:29:16 -0500

Babgen gravatar image

updated 2013-01-27 00:30:05 -0500

Dear all

Does sage support groups such as Frobenius groups or general affine group. How can I find the permutation representation of an arbitrary group.

Best regrad

edit retag flag offensive close merge delete

1 answer

Sort by ยป oldest newest most voted
0

answered 2013-01-27 18:29:47 -0500

benjaminfjones gravatar image

There isn't a general construction of Frobenius groups in Sage currently, although there are many specific ones that can be constructed as members of other collections of groups, e.g. the symmetric group on 3 letters is a Frobenius group:

sage: G = SymmetricGroup(3)

Is it a Frobenius group? Let's check:

for g in G:
    if not g.is_one():
        fixed = [ x for x in [1..3] if g(x) == x ]  
        print "elt: ", g, "fixed set: ", fixed

returns:

elt:  (2,3) fixed set:  [1]
elt:  (1,2) fixed set:  [3]
elt:  (1,2,3) fixed set:  []
elt:  (1,3,2) fixed set:  []
elt:  (1,3) fixed set:  [2]

Yep.

I don't quite understand your second question. Any finite group can be embedded in a permutation group by its left or right action on itself. This is a basic theorem.

edit flag offensive delete link more

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 2013-01-27 00:29:16 -0500

Seen: 193 times

Last updated: Jan 27 '13