What is boundedly?

Some articles on boundedly:

Boundedly Generated Group - Free Groups Are Not Boundedly Generated - Burnside Couterexamples
... 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 generators, and hence for all free groups ... enough to produce one example of a finitely generated group which is not boundedly generated, and any finitely generated infinite periodic group will work ... free groups of rank at least two are not boundedly generated ...
Boundedly Generated Group - Properties
... 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 ... periodic group must be finite if it is boundedly generated equivalently, an infinite finitely generated periodic group is not boundedly generated ...
Boundedly Generated Group - Free Groups Are Not Boundedly Generated - Hyperbolic Geometry
... proof that that G = SL2(Z) is not boundedly generated ... space of pseudocharacters, it cannot be boundedly generated ... to prove that any non-elementary Gromov-hyperbolic group is not boundedly generated ...