The story
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,… each of which may be on or off, with a lamplighter standing at some lamp l_k.
Etymology from Wiktionary, CC BY-SA 4.0.
lamplighter group
Today it means: The restricted wreath product mathbf Z₂≀ mathbf Z. Full definition →