Dear Alireza,
the operation ConjugacyClasses returns the equivalence classes you are
looking for. For each conjugacy class you can get a representative.
gap> g := SL(5,5);;
gap> classes := ConjugacyClasses( g );;
gap> Length( classes );
774
gap> representatives := List( classes, Representative );;
gap> representatives[1];
[ [ Z(5)^0, 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5) ],
[ 0*Z(5), Z(5)^0, 0*Z(5), 0*Z(5), 0*Z(5) ],
[ 0*Z(5), 0*Z(5), Z(5)^0, 0*Z(5), 0*Z(5) ],
[ 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0, 0*Z(5) ],
[ 0*Z(5), 0*Z(5), 0*Z(5), 0*Z(5), Z(5)^0 ] ]
Hope this helps.
Sven.
--
Sven Reichard
School of Mathematics and Statistics
University of Western Australia
arashrafi wrote:
Dear Pubbers,
I am doing some research with the group G=SL(5,5). I need to the
equivalence classes of similarity relation on G. These are the sets
[A] = \{ B^tAB | B \in SL(5,5) \}. How can I get a representative for
any equivalence classes? Is there a GAP command (or a series of
commands) which given a finite matrix group G, would return a chain x_1
, ..., x_t of representatives for the mentioned classes?
Thanks in advance for any help you can provide.
Sincerely,
Alireza
-----------------------------------
Ali Reza Ashrafi,
Professor of Mathematics
Department of Mathematics,
Faculty of Science,
University of Kashan,
Kashan,Iran.
Tel: +98 361 5552935
Fax: +98 361 5552930
Mob: +98 912 5148260
E-mail: [EMAIL PROTECTED]
[EMAIL PROTECTED]
[EMAIL PROTECTED]
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