[GAP Forum] orbits...

Michael Hartley Michael.Hartley at nottingham.edu.my
Thu Jul 8 09:13:25 BST 2004

Dear Forum,

thanks for the advice on the stabilizer bug. I have now upgraded to

On another topic - suppose I want a representative of each orbit of
group acting on a set, without actually finding the whole orbits?
Specifically, I am trying to get Automorphism classes of involutions of
a group.

So far, I do this :

AutomorphismClassesInvolutions := function(grp) # should probably be
called AutomorphismClassRepresentativeInvolutions.
   local ss,inv,cr,au;
   au := AutomorphismGroup(grp);   # find the automorphism group
   ss := SylowSubgroup(grp,2);       # find a sylow 2-subgroup ss
   inv := Filtered(Elements(ss),x -> Order(x) = 2);   # get the
involutions in ss
   cr := List(Orbits(au,inv),Representative);   # get representatives
of the orbits of the involutions under the automorphism group.
   return cr;

Note that the last line before the return will actually compute the
whole Orbit.

I really just want a representative from each orbit. Or is there a
faster way to get the involutions??

Yours, Mike H...

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