Subring subgroups of symplectic groups in characteristic 2
نویسندگان
چکیده
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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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.
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ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2017
ISSN: 1061-0022,1547-7371
DOI: 10.1090/spmj/1459