Growth in solvable subgroups of $GL_r(Z/pZ)$

Jeudi 30 septembre 2010 14:00-15:00 - Gill Nick - University of Bristol

Résumé : This seminar concerns joint work with Helfgott. Let A be a subset of
$GL_r(K)$ for K a finite field. It is conjectured that either A grows rapidly (i.e. $|AAA|>C|A|^1+e$, for some universal constants C,e) or else we are « in the nilpotent setting » (i.e. we reduce to the study of growth inside a nilpotent group).
I outline a recent result which proves this conjecture under thernassumptions that - $K = Z/pZ$ ;
and - the group generated by A is solvable.
(In fact, we can do better than this ; come to the seminar for a precise statement !)

Lieu : bât. 425 - 121-123

Growth in solvable subgroups of $GL_r(Z/pZ)$  Version PDF
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