lamplighter group

Etymology
The group can be viewed as acting on a doubly infinite sequence of street lamps $$\dots,l_{-2},l_{-1},l_0,l_1,l_2,l_3,\dots$$ each of which may be on or off, with a lamplighter standing at some lamp $$l_k$$.

Noun

 * 1)  The restricted wreath product $$\mathbf{Z}_2 \wr \mathbf Z$$.