Boundedly

Boundedly Generated Group - Free Groups Are Not Boundedly Generated - Burnside Couterexamples
... if a single finitely generated group with at least two generators is known to be not boundedly generated, this will be true for the free group on the same number of ... enough to produce one example of a finitely generated group which is not boundedly generated, and any finitely generated infinite periodic group will work ... Consequently, free groups of rank at least two are not boundedly generated ...

Boundedly Generated Group - Free Groups Are Not Boundedly Generated - Hyperbolic Geometry
... There is also a simple geometric proof that that G = SL2(Z) is not boundedly generated ... elements can similarly be used to prove that any non-elementary Gromov-hyperbolic group is not boundedly generated ...

Boundedly Generated Group - Properties
... by passing to a subgroup of finite index if H is a finite index subgroup of G then G is boundedly generated if and only if H is boundedly generated ... Any quotient group of a boundedly generated group is also boundedly generated ... A finitely generated periodic group must be finite if it is boundedly generated equivalently, an infinite finitely generated periodic group is not boundedly generated ...