Growth of Certain Non-positively Curved Cube Groups

• Coxeter groups with respect to the standard generating set [5, p. 45, Exercise 26], the argument being that of Solomon [18]; • virtually abelian groups with respect to any generating set [4]; • two-step nilpotent groups with infinite cyclic commutator subgroup with respect to some generating set [19]. (On the other hand, it is shown in [19] that if G has Heisenberg rank at least 2, then G has a finite generating set A such that G has transcendental growth with respect to A! In particular, all higher discrete Heisenberg groups H2, H3, . . . possess transcendental growth series.) • solvable Baumslag–Solitar groups 〈x, y|xyx−1 = yb〉 with respect to a generating set 〈x, y〉 [9]; • amalgam groups (= colimits) of certain non-positively curved triangles of groups [10].