Transitive subgroup of symmetric group: Difference between revisions
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==Definition== | ==Definition== | ||
Let <math>S_n</math> be the [[symmetric group]] on <math>n</math> letters. Let it act naturally on <math>X=\{ 1, 2, \dots, n \}</math>. A subgroup <math>G \leq S_n</math> is said to be a '''transitive subgroup of the symmetric group on n letters''' if its action on <math>X</math> made from the restriction of the action of <math>S_n</math> on <math>X</math> is a [[transitive group action]]. | Let <math>S_n</math> be the [[symmetric group]] on <math>n</math> letters. Let it act naturally on <math>X=\{ 1, 2, \dots, n \}</math>. A subgroup <math>G \leq S_n</math> is said to be a '''transitive subgroup of the symmetric group on n letters''' if its action on <math>X</math> made from the restriction of the action of <math>S_n</math> on <math>X</math> is a [[transitive group action]]. | ||
Revision as of 12:55, 20 November 2023
This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition
Let be the symmetric group on letters. Let it act naturally on . A subgroup is said to be a transitive subgroup of the symmetric group on n letters if its action on made from the restriction of the action of on is a transitive group action.