lamplighter group

The group can be viewed as acting on a doubly infinite sequence of street lamps ${\displaystyle \dots ,l_{-2},l_{-1},l_{0},l_{1},l_{2},l_{3},\dots }$ each of which may be on or off, with a lamplighter standing at some lamp ${\displaystyle l_{k}}$.

lamplighter group (plural lamplighter groups)

1. (group theory) The restricted wreath product ${\displaystyle \mathbf {Z} _{2}\wr \mathbf {Z} }$.