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 regrad
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
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.
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Asked: 2013-01-27 07:29:16 +0100
Seen: 442 times
Last updated: Jan 28 '13