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If $G$ is a linear group over a ring $R$, is every homomorphic image of $G$ again a linear group?

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    What exactly do you mean by "linear group over a ring"? A subgroup of the endomorphisms of $R^n$?2012-08-24
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    $G$ islinear if it is a subgroup of $GL(n,R)$ for some $n$ and some ring $R$.2012-08-24
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    You mean "commutative ring". Because every group $G$ is a subgroup of $GL_1(\mathbf{Z}G)$, where $\mathbf{Z}G$ is its group algebra.2012-08-25

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