lamplighter group

Meaning

Noun

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

Origin

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 $l_k$ .

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