| 释义 |
orbit-stabilizer theorem For a finite group G acting on a finite set S, and s ∈ S, the product of the cardinality of the orbit of s and the order of the stabilizer of s equals the order of G. For example, the rotational symmetry group of a cube acts transitively on its six faces; so taking s to be any face, there is one orbit of size 6 and the stabilizer has order 4 (the rotations through the face's midpoint). Hence the rotational symmetry group has order 6 × 4 = 24.
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