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...
متن کاملLifting Witt Subgroups to Characteristic Zero
Let k be a perfect field of characteristic p > 0. Using Dieudonné modules, we describe the exact conditions under which a Witt subgroup, i.e., a finite subgroup scheme of Wn, lifts to the ring of Witt Vectors W (k).
متن کاملGenerating Dense Subgroups of Measure Preserving Transformations
Except for a set of first category, all pairs of measure preserving transformations generate a dense subgroup of G, the group of all invertible measure preserving transformations of the unit interval when G has the weak topology. Consider G the group of invertible (Lebesgue) measure preserving transformations of the unit interval onto itself. On G, we put the weak topology (Halmos [2, pp. 61-67...
متن کاملLIFTING SUBGROUPS OF SYMPLECTIC GROUPS OVER Z/lZ
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.
متن کاملLifting Free Subgroups of PSL(2, R) to Free Groups
Let F = 〈a, b〉 be a rank two free group, let G = 〈A,B〉 be a two generator subgroup of PSL(2,R) and let ρ be a faithful representation of F with ρ(a) = A and ρ(b) = B. If G is discrete and free, many results about the primitive elements of G are proved using the geometry that G inherits from PSL(2,R), the group of orientation preserving isometries of the hyperbolic plane. Some of these results c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03917-8