lamplighter group

== English == === Etymology === The group can be viewed as acting on a doubly infinite sequence of street lamps … , l − 2 , l − 1 , l 0 , l 1 , l 2 , l 3 , … {\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 l k {\displaystyle l_{k}} . === Noun === lamplighter group (plural lamplighter groups) (group theory) The restricted wreath product Z 2 ≀ Z {\displaystyle \mathbf {Z} _{2}\wr \mathbf {Z} } .