> < ^ Date: Mon, 08 Dec 2003 10:25:07 -0700 (MST)
< ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
> < ^ Subject: Re: Cycle Structure and Orbital Transversal

Dear GAP-Forum,

Bruce Colletti wrote:
> Is there a GAP command that tests whether two permutations have the same =
> cycle structure?
There is CycleStructurePerm that returns the cycle structure (in a slightly
encoded form):

gap> CycleStructurePerm((2,3)(5,6,7,8)(9,10)); 
[ 2,, 1 ]
(two 2-cycles, one 4-cycle)

What command (if any) returns a transversal on the orbits of a group =
action? At present, I simply build a transversal by grabbing each =
orbit's first element. Am hoping there's a better way.

To get representatives of the orbits you need some information about the
orbits. If the domain is not to large, I would use:

If the domain is too large to be listed, it might be possible to compute
stabilizers (and thus orbit lengths) and to do backtrack conjugacy tests and
thus eventually find sufficiently many orbit representatives. The best
approach depends very much on the kind of action. Without knowing this it is
hard to give a better response.

(One particular case of this problem is the action of a group on
itself by conjugation, the result are the conjugacy classes. There are a
handful of papers that deal with this problem and the code is quite
nontrivial. It is therefore unlikely to have a good more ``general''

Matt Insall responded:

Why am I getting these in a weird format? I joined the GAP listserve
recently, and I would like to get the messages in the format intended by the

The program that runs the forum email list dates from the early 1990s and
reproduces emails verbatim as text as was the email standard at that time.

MIME encoduing and attachments are newer technologies that use the email
format for a wrapper of files. the gap-forum list fill still reproduce the
text content (which is the MIME encoded version) but does not know what to
do with the MIME version.

In short, MIME encoded email will not be forwarded correctly.

Some email programs unfortunately use this to wrap every mail by default
into HTML and that is what we are seeing with this email.

Best wishes,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288

Miles-Receive-Header: reply

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