Detecting linear dependence on multiplicative groups - MathOverflow 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 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>