stabilizer subgroup

noun

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.

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Meanings

nounstabilizer subgroup (plural stabilizer subgroups)

plural stabilizer subgroups

  1. algebraSaid 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. algebraSaid 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.
Cite this entry
APA

stabilizer subgroup. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/stabilizer%20subgroup

MLA

“stabilizer subgroup.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/stabilizer%20subgroup. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “stabilizer subgroup,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/stabilizer%20subgroup.

Source: stabilizer subgroup on Wiktionary, CC BY-SA 4.0.