Finite Approximations to Lie Groups

  title={Finite Approximations to Lie Groups},
  author={A. Turing},
  journal={Annals of Mathematics},
  • A. Turing
  • Published 1938
  • Mathematics
  • Annals of Mathematics
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
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