On linear combinatorics I. Concurrency—An algebraic approach

This article is the first one in a series of three. It contains concurrency results for sets of linear mappings of ℝ with few compositions and/or small image sets. The fine structure of such sets of mappings will be described in part II [3]. Those structure theorems can be considered as a first attempt to find Freiman-Ruzsa type results for a non-Abelian group. Part III [4] contains some geometric applications.