Math 2.0

example

Orders of the elements of S3

Example

The symmetric group S3S_3 has order 66. The identity has order 11. Each transposition (1 2)(1\,2), (1 3)(1\,3) and (2 3)(2\,3) has order 22. Each 33-cycle (1 2 3)(1\,2\,3) and (1 3 2)(1\,3\,2) has order 33. Each of the orders 11, 22 and 33 divides 66, as the result on element orders states.

Remarks

No element has order 66, so S3S_3 is not cyclic.

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Sources

  1. Web https://en.wikipedia.org/wiki/Order_(group_theory), Example

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