LIFTING SUBGROUPS OF SYMPLECTIC GROUPS OVER Z/lZ
نویسندگان
چکیده
For a positive integer g, let Sp 2g(R) denote the group of 2g × 2g symplectic matrices over a ring R. Assume g ≥ 2. For a prime number l, we show that any closed subgroup of Sp 2g(Zl) that surjects onto Sp2g(Z/lZ) must in fact equal all of Sp2g(Zl). Our result is motivated by group theoretic considerations that arise in the study of Galois representations associated to abelian varieties.
منابع مشابه
Lifting subgroups of symplectic groups over
For a positive integer g, let Sp2g(R) denote the group of 2g× 2g symplectic matrices over a ring R. Assume g ≥ 2. For a prime number , we give a self-contained proof that any closed subgroup of Sp2g(Z ) which surjects onto Sp2g(Z/ Z) must in fact equal all of Sp2g(Z ). The result and the method of proof are both motivated by group-theoretic considerations that arise in the study of Galois repre...
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