stabilizer subgroup

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|algebra}} ''Said of a [[group action|group acting]] on a set, and with respect to an element of that set'': the subgroup of the given group whose action leaves that element [[fixed point|fixed]].
2. {{lb|en|algebra}} ''Said of a [[group action|group acting]] on a set, and with respect to a subset of that set'': the subgroup of the given group for which the image of the set under the group action is a subset of the original set. Some authors instead define this to be the subgroup of the given group whose action leaves each element of the subset fixed.

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