ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 28 Jan 2013 01:29:47 +0100permutation representationhttps://ask.sagemath.org/question/9747/permutation-representation/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 regradSun, 27 Jan 2013 07:29:16 +0100https://ask.sagemath.org/question/9747/permutation-representation/Answer by benjaminfjones for <p>Dear all</p>
<p>Does sage support groups such as Frobenius groups or general affine group. How can I find the permutation representation of an arbitrary group.</p>
<p>Best regrad</p>
https://ask.sagemath.org/question/9747/permutation-representation/?answer=14493#post-id-14493There 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.Mon, 28 Jan 2013 01:29:47 +0100https://ask.sagemath.org/question/9747/permutation-representation/?answer=14493#post-id-14493