Growth and cogrowth of normal subgroups of a free group

Abstract

We give a sufficient condition for a sequence of normal subgroups of a free group to have the property that both, their growths tend to the upper bound and their cogrowths tend to the lower bound. The condition is represented by planarity of the quotient graphs of the tree.

References in corpus (2)

• Recurrence and pressure for group extensions
• Normalizer, divergence type and Patterson measure for discrete groups of the Gromov hyperbolic space