What exactly does $\text{Aff}(2) = \mathbb{R}^2 \rtimes SL_{2}(\mathbb{R})$ mean? I know that it is the group of area preserving affine transformations of (oriented) $\mathbb{R}^2$. But how would you interpret the $\rtimes$ symbol?
Interpretation of Symbol: "$\rtimes$"
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$\begingroup$
abstract-algebra
group-theory
notation
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2It is semidirect product. Look up up on [wikipedia](http://en.wikipedia.org/wiki/Semidirect_product). (Basically, it is a generalisation of direct product. In a direct product you have two subgroups $H, K\lhd G$, $G=HK$ and $H\cap K=1$. In a semidirect product, only one of $H$ and $K$ is necessarily normal. It is helpful to know what a [group action](http://en.wikipedia.org/wiki/Group_action) is, as the non-normal group acts on the normal one via a non-trivial action.) – 2012-12-21
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0@user1729: What is both subgroups are normal? Are groups that can be "factored" into two normal subgroups better than groups that cannot? – 2012-12-21
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0I've expanded a bit on this in my answer, below. – 2012-12-21
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15It is a symbol used on maps of highways to show that a rest stop does have picnic tables, but indicating that some of the tables have been pushed over by vandals. – 2012-12-21
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0@amWhy: There's no need to add [abstract-algebra] to posts tagged group theory, unless they fundamentally speak about objects other than groups. See [this meta thread](http://meta.math.stackexchange.com/q/11050/622). – 2013-11-07
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0Okay, @Asaf. Thanks for the link to the thread! – 2013-11-07