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- W2092183032 abstract "It is known from group theory that multiplication tables for finite groups are Latin squares. These basic Latin squares have proved useful for solving various problems, for example, problems of memory management in parallel computing systems, organizing party games, communications networking, computer imaging, and experimental design. We show how the problem of multiplication tables for a finite group G of order N can be solved using APL. The solution is based on Lagrange's and Cayley's theorems for finite groups: the order of a subgroup of a finite group G is a divisor of the order of the group and every group G of order N is isomorphic with a subgroup of the group of permutations of N objects (symmetric group SN). We demonstrate that using APL interactively offers a powerful, consistent, and simple notation for dealing with the elements of the symmetric group SN. Group tables for the groups of order 4, 6, and 8 are used to illustrate the method. Possible simplifications of the method are outlined." @default.
- W2092183032 created "2016-06-24" @default.
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- W2092183032 date "2003-06-11" @default.
- W2092183032 modified "2023-09-24" @default.
- W2092183032 title "Finite group tables in APL" @default.
- W2092183032 cites W2086665685 @default.
- W2092183032 doi "https://doi.org/10.1145/882067.882078" @default.
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