Thank you Mr Mears, 
If I understand correctly, to execute the combination of symmetries I must to 
add all the relevant declarations of symmetries to the same object Symmetries 
s. 
and the execution of the combination is done sequentially, So, we have the 
execution of the first decalaration symmetry is done and next the second 
definition of symmetry is executed ...etc, but they do not run in parrallel. 

So to apply the combination of the following symmetric group: 
Gn = { sym 1: 'interchangeability of specified rows' + sym 2: 
'interchangeability of specified columns' + sym 3: 'rotation of rows'} * { 
symmetry identity, sym 4: 'reflections of columns of a matrix' }.
I have to execute the following pseudo code: ( post all definitions of 
symmetries to the same object s )
Symmetries s;
s << declaration_of_sym 1;
branch (......,sym 1, ....);
s << declaration_of_sym 2;
branch (....., sym 2, ....);
s << declaration_of_sym 3;
branch (....., sym 3, ....);

s << declaration_of_sym 4;
branch (....., sym 4, ....);

thank you sir,
Best regards. sabrina.
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