  This paper presents a study of the asymptotic geometry of groups with
contracting elements, with emphasis on a subclass of statistically
convex-cocompact (SCC) actions. The class of SCC actions includes relatively
hyperbolic groups, CAT(0) groups with rank-1 elements and mapping class groups,
among others. We exploit an extension lemma to prove that a group with SCC
actions contains large free sub-semigroups, has purely exponential growth and
contains a class of barrier-free sets with a growth-tight property. Our study
produces new results and recovers existing ones for many interesting groups
through a unified and elementary approach.
