on permutations and lie algebras

if we reanalyze turings final argument can we say that he is testing for a given representation being one that is a group, given a lie algebra and its generator?  

he really says that g has subgroup h which inturn has a centralizer subgroup h1
see http://www.turingarchive.org/viewer/?id=133&title=29

see also k:

Generalization to Borel setsEdit

This distribution can be generalized to more complicated sets than intervals. If S is a Borel set of positive, finite measure, the uniform probability distribution on S can be specified by defining the pdf to be zero outside S and constantly equal to 1/K on S, where K is the Lebesgue measure of S

from https://en.m.wikipedia.org/wiki/Uniform_distribution_(continuous)

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