Math 2.0

Group theory and generalizations Example

Orders of the elements of S3

Builds on Symmetric groupOrder of an element

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.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

Show the path as a graph
Group, concept, no evidence levelGroupconceptSymmetric group, concept, no evidence levelSymmetric groupconceptLaws of exponents in a group, statement, no evidence levelLaws of exponents in …statementOrder of an element, definition, no evidence levelOrder of an elementdefinitionOrders of the elements of S3, example, no evidence levelOrders of the element…example
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Group concept
  2. Symmetric group concept
  3. Laws of exponents in a group statement
  4. Order of an element definition
  5. Orders of the elements of S3 example

Further reading

  1. Web https://en.wikipedia.org/wiki/Order_(group_theory), Example
About this page
TagY20PEX049W
URIm2://Y20PEX049W
Kindexample
WritingW0 stub
MSC20D60
Instance ofOrder of an element
IllustratesOrder of an element divides the order of the group
UsesSymmetric group, Order of an element

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.