[GAP Forum] Product of complexes

[Rudolf Zlabinger]

Dear Forum,

does anybody know a GAP function to directly calculate the product of complexes of groups or semigroups, that means the set of the ordinary products of the cartesian product of subsets of elements of a group as outlined in the trivial example below:

a4:=AlternatingGroup(4);;
a5:=AlternatingGroup(5);;
# as examples of subsets taken as lists

a4a5:=AsSet(List(Cartesian(AsList(a4),AsList(a5)),Product));; 
# this is a circumscription of the function I am looking for

groupa4a5:=AsGroup(a4a5);;        
# in this case, the result is a group, of course

StructureDescription(groupa4a5); 
"A5"                                          
# of course, as a4 is a subgroup of a5

The subsets has not to be subgroups or groups as in the example above, rather any ordinary sets of group elements.

Thank you, Rudolf Zlabinger