Return to Revisions

I believe the substance of the question has been answered, but since it's a question of what can be done without modern machinery, this may help: I was thinking about the problem of deducing structure of a group from the growth rate in the '70's, when Gromov was still in Russia. When we first met, soon after he arrived, we had much in common that we'd been thinking about, but he had not yet proven the theorem concerning groups of polynomial growth. I was stuck on trying to analyze groups of quadratic growth; I recall that strictly linear growth seemed fairly straightforward using the technology of the time: in particular, Stalling's idea of a minimizing cocyle (from his work analying ends of groups). I'm pretty sure there's a fairly elementary complete proof based on that, just thinking of components of the sphere of radius R as defining a cocycle. I could supply details on demand.