Math 2.0

Group theory and generalizations Proposition

Order of the symmetric group

Builds on Symmetric groupOrder of a group

Statement

Let nn be a positive integer. The symmetric group SnS_n has order n!n!.

Remarks

A permutation σ\sigma has nn choices for σ(1)\sigma(1), then n−1n - 1 choices for σ(2)\sigma(2), and so on, down to 11 choice for σ(n)\sigma(n). For example, ∣S3∣=6|S_3| = 6 and ∣S4∣=24|S_4| = 24.

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Group, concept, no evidence levelGroupconceptOrder of a group, definition, no evidence levelOrder of a groupdefinitionSymmetric group, definition, no evidence levelSymmetric groupdefinitionOrder of the symmetric group, statement, no evidence levelOrder of the symmetri…statement
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  1. Group concept
  2. Order of a group definition
  3. Symmetric group definition
  4. Order of the symmetric group statement

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Further reading

  1. Web https://en.wikipedia.org/wiki/Symmetric_group, lead section
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Tag0PCKBBMEXC
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Kindstatement, proposition
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MSC20B30
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UsesSymmetric group, Order of a group

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