GL IAPS

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

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Definition

The GL IAPS, or general linear IAPS or IAPS of general linear groups associated to a unital ring $R$ is an IAPS of groups where:

• The $n^{th}$ member is the group $GL_{n}(R)$ of invertible matrices with entries in $R$, of order $n$

• The block concatenation map $\Phi _{m,n}(A,B)$ yields:

$\Phi _{m,n}(A,B)={\begin{pmatrix}A&0\\0&B\end{pmatrix}}$