Growth and cogrowth of normal subgroups of a free group

Jaerisch, Johannes; Matsuzaki, Katsuhiko

doi:10.1090/proc/13568

Growth and cogrowth of normal subgroups of a free group
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by Johannes Jaerisch and Katsuhiko Matsuzaki PDF

Proc. Amer. Math. Soc. 145 (2017), 4141-4149 Request permission

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.

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