Multiply Transitive Lie Group of Transformations as a Physical Structure

Abstract We establish a connection between physical structures and Lie groups and prove that each physical structure of rank $$(n+1,2)$$ , $$n\in \mathbb {N} $$ , on a smooth manifold is isotopic to an almost $$n $$ -transitive Lie group of transformations. We also prove that each almost $$n$$ -transitive Lie group of transformations is isotopic to a physical structure of rank $$(n+1,2) $$ .