Cocroissance Des Groupes A Petite Simplification

Let be a group presented by e₁,...,e_m|r₁,...,r_k, L the freegroup generated by e₁,...,e_m, and N = Ker(L). Let c_n be thenumber of elements of length n in N. We know that c = lim sup(c_n)^1/n exists and that (2m–1) < c 2m – 1. ifN {1}. We prove that if the group satisfies a condition slightlyweaker than the small cancellation condition C^'() with <1/6, then c(2m–1) when the lengths of the relations r_itend to infinity. A consequence of this result is a theoremof Grigorchuk.