Today I attended a course on Geometric Group Theory in Spanish, and we saw an example of a group which could be literally translated as "bluffer's group", because there is a funny way to interpret it. The group is the following:
$\mathbb{Z}/2\mathbb{Z}[t,t^{-1}]\rtimes \langle t\rangle$
Where the product is defined by
$(p(t), t^m)(q(t),t^n)=(p(t)+t^mq(t),t^{m+n})$.
What's the actual name of this group in English?