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one of the more challenging aspects of mathematics is trying to figure out a way of representing something and so with groups one of the ways we do that is we represent groups using a multiplication table so this is a fairly common way of representing small groups its not quite as useful once our groups have like thousands of elements but so that we can construct these multiplication tables so for example lets say I have a group with three elements and it has to have an identity Ill call that E and I have two other elements a and B and because it has three elements a and B have to actually be different elements that kind of sounds obvious but as well see thats a little bit tricky so we can represent the group by giving the table of all possible products of the elements so what I have is Ill set up my multiplication table I have by three elements e a and B a and B and Im going to set up this table for this product P times now remember its important that the its important to ke
