In your IF statement, the following is not a valid SQL statement:
UPDATE `Error: deletion RootGroup is prohibited!`;
This should be this:
IF old.parent_group=old.PKey THEN
UPDATE `Error: deletion RootGroup is prohibited!` set x=1;
ELSE
UPDATE groups
SET parent_group=old.parent_group
WHERE parent_group=old.PKey;
END IF;
I have never done things this way. It is a bit of an ugly way of doing it. But if it works, what the heck.