= Affine group
{title2=$\operatorname{Aff}(V)=V\rtimes\operatorname{GL}(V)$}
{wiki}
For a finite-dimensional <vector space> $V$, the affine group consists of invertible <affine maps> $x\mapsto Ax+b$, where $A$ belongs to the <general linear group> and $b\in V$. Its product is $(A,b)(A',b')=(AA',b+Ab')$, making it the <semidirect product> of the translation vector space and its general linear group. On the real line the positive-dilation subgroup is the <real affine group> used in the adjacent article.
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