# Finite Approximations to Lie Groups

@article{Turing1938FiniteAT, title={Finite Approximations to Lie Groups}, author={A. Turing}, journal={Annals of Mathematics}, year={1938}, volume={39}, pages={105} }

A certain sense in which a finite group may be said to approximate the structure of a metrical group will be discussed. On account of Jordan's theorem on finite groups of linear transformations' it is clear that we cannot hope to approximate a general Lie group with finite subgroups. I shall show that we cannot approximate even with groups which are 'approximately subgroups': in fact the only approximable Lie groups are the compact Abelian groups. The key to the situation is again afforded by… Expand

#### 206 Citations

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