most recent 30 from http://mathoverflow.net 2013-05-25T02:53:24Z http://mathoverflow.net/feeds/question/86237 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/86237/detecting-linear-dependence-on-multiplicative-groups Tzanko Matev 2012-01-20T17:59:25Z 2012-01-20T17:59:25Z

<p>Let G = $\mathbb{G}_m^2/\mathbb{Q}$ and let $\Gamma \subseteq G(\mathbb{Q})$ be a free abelian group of rank 2. Assume that the set of primes $p$ for which $\Gamma \mod p$ is cyclic has positive density. Does this imply that $\Gamma$ is contained in a proper algebraic subgroup of G?</p>