[GAP Forum] List of elements

[Alireza Abdollahi]

Dear Pubbers
I  typed the following commands:

gap> W:=WreathProduct(SymmetricGroup(3),CyclicGroup(4));;
gap> ele:=Elements(W);;
gap>x:=ele[4];
gap>y:=ele[228];

Here are my questions:

If I end the above GAP session and again (after some while!) open a new session 
and repeat the commands above, 

should I get the same x and y as the  first time? if so, is this a general rule 
(at least for the above commands)?

Actually, I would like to use the above form in a research article, so the doubt 
is whether the above question has positive answer or not?! My experience show 
that we always get the same for x and y or some other element!
Of course, I know that the best/worst way is to locate the elements x and y  in 
W by fixing a generating set for W and then I do not cite GAP, which is not 
fair!!
Sorry in advance, if my question is very stupid; and thanks for any friendly 
help.
All the Best
Alireza Abdollahi






 Alireza Abdollahi
Department of Mathematics
University of Isfahan 
Isfahan 81746-73441,Iran
a.abdollahi at math.ui.ac.ir
abdollahi at member.ams.org
http://sci.ui.ac.ir/~a.abdollahi