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Keyword:

orbit-stabilizer

orbit-stabilizer theorem

Noun

uncountable

(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.

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。

What is this buttons?

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.

Google Translation / DeepL Translation

軌道安定化群定理を適用すると、群の作用による各元の軌道とその元の安定化群の余類との間に自然な全単射が成り立ち、軌道の数え上げが容易になります。

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