# Permutation IAPS

From Groupprops

*This article describes a particular IAPS of groups, or family of such IAPSes parametrized by some structure*

## Definition

### Symbol-free definition

The permutation IAPS is an IAPS of groups where the member is the symmetric group , and where the block concatenation map is defined as the permutation that permutes the first symbols according to the permutation in and the next symbols according to the permutation in .

### Definition with symbols

The permutation IAPS is an IAPS of groups where the member is and the block concatenation map is defined as follows:

Given a permutation and a permutation , the permutation is defined as the following permutation on . It sends to , and sends to .

## Examples

As an example, consider , . Let , and . Then: