stabilizer subgroup

English

Noun

stabilizer subgroup (plural stabilizer subgroups)

  1. (algebra) Said of a 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.
  2. (algebra) Said of a 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.

Derived terms

Further reading

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