Last Updated
：2025/12/04
orbit-stabilizer theorem
Noun
uncountable
Japanese Meaning
群がある集合に作用するとき、その集合の各要素について、その要素の軌道とその要素を固定する安定化部分群の余剰集合とが自然な全単射であることを示す代数学の定理。
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(algebra) A theorem which states that for each element of a given set that a given group acts on, there is a natural bijection between the orbit of that element and the cosets of the stabilizer subgroup with respect to that element.
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orbit-stabilizer theorem
When applying the orbit-stabilizer theorem, we can establish a natural bijection between each element's orbit under the group action and the cosets of its stabilizer subgroup, which simplifies counting orbits.
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When applying the orbit-stabilizer theorem, we can establish a natural bijection between each element's orbit under the group action and the cosets of its stabilizer subgroup, which simplifies counting orbits.
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