Permutation IAPS

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 $n^{th}$ member is the symmetric group $S_n$, and where the block concatenation map $S_m$ × $S_n$ → S_{m+n} is defined as the permutation that permutes the first $m$ symbols according to the left argument and the next $n$ symbols according to the second argument.

Definition with symbols

The permutation IAPS is an IAPS of groups where the $n^{th}$ member is $S_n$ and the block concatenation map ${\mathrm{\Phi }}_{m,n}:S_m\times S_n\to S_{m+n}$ is defined as follows:

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