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 $G{L}_n(R)$ of invertible matrices with entries in $R$, of order $n$

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

${\mathrm{\Phi }}_{m,n}(A,B)=\left(\begin{array}{cc}A& 0\\ 0& B\end{array}\right)$