# Transpositions of adjacent elements generate the symmetric group on a finite set

From Groupprops

## Statement

Let be a totally ordered finite set. Then, the set of Transposition (?)s between adjacent elements in the total ordering of generates the Symmetric group (?) on .

Note that any totally ordered set can be identified with the set with the usual integer ordering, so the above can be rephrased as: the set of transpositions of the form generate the symmetric group on .

It turns out that this generating set is both Sims-reduced and Jerrum-reduced.

## Related facts

## Proof

### The bubble sort proof

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