Dear Forum,
the inquiry is already answered, of course, the sequence in question is not
needed at all.
Thanks to the contributors, all the best, Rudolf Zlabinger
----- Original Message -----
From: "Rudolf Zlabinger" <[EMAIL PROTECTED]>
To: "GAP Forum" <[EMAIL PROTECTED]>
Sent: Sunday, June 10, 2007 9:38 AM
Subject: [GAP Forum] IsInnerProduct
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
--------------------------------------------------------------------------------
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