[GAP Forum] Similarity

[Sven Reichard]

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,
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