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when you learned arithmetic you probably had to memorize a multiplication table this table shows you how to multiply any two small numbers usually the integers one through twelve in abstract algebra you begin to work with new types of numbers groups behave very differently than the numbers in arithmetic so when youre first starting out in abstract algebra its helpful to go back to the basics and make a group multiplication table group multiplication tables are sometimes called kali tables in honor of the british mathematician arthur cayley because he was the first to use them in a math paper they work just like the multiplication tables from arithmetic lets see a simple example and then look at how kb tables can be used to explore small groups consider the group under multiplication consisting of these four elements 1 negative 1 i and negative i its traditional to put the group operation in the upper left corner next list the elements in the same order in the header row and header
