# 點燈夫群

$\left(\bigoplus_{\mathbb Z} (\mathbb Z/2\mathbb Z)\right)\rtimes \mathbb Z$

$\langle a, t\mid a^2 , [t^i a t^{-i}, t^j a t^{-j}], i,j\in \mathbb Z \rangle$

## 參考

1. ^ Cleary, Sean; Taback, Jennifer. Metric properties of the lamplighter group as an automata group. Geometric methods in group theory. Providence, RI: Amer. Math. Soc.. 2005: pp. 207-218.
2. ^ V. A. Kaimanovich and A. M. Vershik. Random Walks on Discrete Groups: Boundary and Entropy. Annals of Probability. 1983, 11 (3): 457–490.