Applications of Groups
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.
KeywordsSymmetry Group Irreducible Representation Conjugacy Class Invariant Subspace Image Parameter
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