Transitive subgroup of symmetric group: Difference between revisions

Revision as of 12:54, 20 November 2023

Definition

Let $S_{n}$ be the symmetric group on $n$ letters. Let it act naturally on $X = {1, 2, \dots, n}$ . A subgroup $G \leq S_{n}$ is said to be a transitive subgroup of the symmetric group on n letters if its action on $X$ made from the restriction of the action of $S_{n}$ on $X$ is a transitive group action.

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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 transitive 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]].