Geodesic
Approximation by p-adic Lie Groups
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 231-239

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DOI

We discuss classes of topological groups which can be approximated by p-adic Lie groups, and varieties of Hausdorff groups generated by classes of \hboxp-adic Lie groups (for a single or multiple p). We give several characterizations of locally compact pro-p-adic Lie groups and locally compact pro-discrete groups, and prove a “pro-version” of Cartan's Theorem: whenever a locally compact group is a pro-p-adic Lie group and a pro-q-adic Lie group for distinct primes p and q, it is pro-discrete. If a locally compact group can be approximated by p-adic Lie groups for variable primes p, then it is a pro-p-adic Lie group for some prime p. 
Glöckner, Helge. Approximation by p-adic Lie Groups. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 231-239. doi: 10.1017/S0017089502020049
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     author = {Gl\"ockner, Helge},
     title = {Approximation by p-adic {Lie} {Groups}},
     journal = {Glasgow mathematical journal},
     pages = {231--239},
     year = {2002},
     volume = {44},
     number = {2},
     doi = {10.1017/S0017089502020049},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502020049/}
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