[GAP Forum] IsInnerProduct

[Rudolf Zlabinger]

Dear Forum,

does anybody know a better performing method than this sequence

prods:=List(Cartesian(subgroup1,subgroup2),Product);
if Length(AsSet(prods)) <> outsize then return false;fi;

in the function

IsInnerProduct:=  function(outergroup,subgroup1,subgroup2)

local outsize,subsize1,subsize2,prods
;

if not IsSubgroup(outergroup,subgroup1) then return false;fi;
if not IsSubgroup(outergroup,subgroup2) then return false;fi;
if Intersection(subgroup1,subgroup2) <> Group(()) then return false;fi;

outsize:=   Size(outergroup);
subsize1:=  Size(subgroup1);
subsize2:=  Size(subgroup2);

if outsize <> subsize1*subsize2 then return false;fi;

prods:=List(Cartesian(subgroup1,subgroup2),Product);

if Length(AsSet(prods)) <> outsize then return false;fi;

return true;

end;

.

The function should return true iff the subgroups subgroup1 and subgroup2 
form a inner product for group outergroup.

Thank you for your cooperation, Rudolf Zlabinger