Zariski dense subgroups of arithmetic groups
Reads0
Chats0
TLDR
In this paper, two commuting semisimple elements of S&(Z) (n 24) which generate a free abelian group of rank 2 and which are contained in a Zariski dense (in fact, maximal) subgroup of infinite index in S&Z are exhibited.About:
This article is published in Journal of Algebra.The article was published on 1987-07-01 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Index of a subgroup & Borel subgroup.read more
Citations
More filters
Journal ArticleDOI
Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity
TL;DR: A substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s were established in this article.
Posted Content
Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity
TL;DR: A 30-year old conjecture of Gregory Margulis and Robert Zimmer on the commensurated subgroups of S-arithmetic groups has been investigated in this article, where the conjecture was shown to be false.
Journal ArticleDOI
Arithmeticity of Certain Symplectic Hypergeometric Groups
Sandip Singh,T. N. Venkataramana +1 more
TL;DR: In this article, the authors give a sufficient condition on a pair of integral polynomials that the associated hypergeometric group is an arithmetic subgroup of the integral symplectic group.
Journal ArticleDOI
Arithmeticity of certain symplectic hypergeometric groups
Sandip Singh,T. N. Venkataramana +1 more
TL;DR: In this article, the authors give a sufficient condition on a pair of polynomials that the associated hypergeometric group is an arithmetic subgroup of the integral symplectic group.
Journal ArticleDOI
Nonarithmetic superrigid groups: Counterexamples to Platonov's conjecture
TL;DR: In this paper, counterexamples to Platonov's Conjecture were constructed, showing that "most" arithmetic groups are superrigid and that finitely generated linear groups which are super-rigid must be of "arithmetic type".
References
More filters
Book
Discrete subgroups of Lie groups
TL;DR: In this paper, the existence of lattices in semisimple Lie groups has been studied and the density theorem of Borel has been proved for non-potent Lie groups.
Journal ArticleDOI
Free subgroups in linear groups
TL;DR: In this paper, the authors consider the problem of finding a non-abelian free group with a solvable normal subgroup R such that R is locally finite (i.e., every jinite subset generates a $nite subgroup).
Journal ArticleDOI
Strong approximation for Zariski-dense subgroups of semi-simple algebraic groups
TL;DR: In this paper, the authors consider algebraically closed fields of characteristic different from 2 and 3, and define algebraic groups over these fields, where G is a simple, connected and simply connected algebraic group defined over k.