Resumo

LOZANO-ROBLEDO, Álvaro. On certain closed subgroups of SL (2, Z_p[[X]]). Rev.colomb.mat. [online]. 2005, vol.39, n.1, pp.13-19. ISSN 0034-7426.

Let p > 2 be a prime number and let Λ = Z_p[[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; Z_p) 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.

Palavras-chave : Closed subgroups; special linear group; Iwasawa algebra.

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