Girth in GF(q)-representable matroids.

Abstract

We prove a conjecture of Geelen, Gerards, and Whittle that for any finite field GF $(q)$ and any integer $t$, every cosimple GF ( $q$ )-representable matroid with sufficiently large girth contains either $M\left(K_t\right)$ or $M\left(K_t\right)^*$ as a minor.