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On certain closed subgroups of SL (2, Zp[[X]])
Let p > 2 be a prime number and let Λ = Zp[[X]] be the ring of power series with p-adic integer coefficients. The special linear group of matrices SL(2, Λ) is equipped with several natural projections. In particular, let πX: SL(2, Λ) → SL(2; Zp) be the natural projection which sends X → 0. Suppose that G is a subgroup of SL(2; Λ) such that the projection H = πX(G) is known. In this note, different criteria are found which guarantee that the subgroup G of SL(2; Λ) is "as large as possible", i.e. G is the full inverse image of H. Criteria of this sort have interesting applications in the theory of Galois representations.
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| Main Author: | |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2005
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| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262005000100002 |
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