Abstract
We now turn to some applications of group theory. The first application makes use of the observation that computing in ℤ can be replaced by computing in ℤn, if n is sufficiently large; ℤn can be decomposed into a direct product of groups with prime power order, so we can do the computations in parallel in the smaller components. In §25, we look at permutation groups and apply these to combinatorial problems of finding the number of “essentially different” configurations, where configurations are considered as “essentially equal” if the second one can be obtained from the first one, e.g., by a rotation or reflection.
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© 1998 Springer Science+Business Media New York
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Lidl, R., Pilz, G. (1998). Applications of Groups. In: Applied Abstract Algebra. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2941-2_6
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DOI: https://doi.org/10.1007/978-1-4757-2941-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3117-7
Online ISBN: 978-1-4757-2941-2
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