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.References
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Additional Information
- Johannes Jaerisch
- Affiliation: Shimane University, Nishi-Kawatsu-cho 1060, Matsue, Shimane 690-8504, Japan
- MR Author ID: 907537
- Katsuhiko Matsuzaki
- Affiliation: Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shiujuku, Tokyo 169-8050, Japan
- MR Author ID: 294335
- ORCID: 0000-0003-0025-5372
- Received by editor(s): December 15, 2015
- Received by editor(s) in revised form: September 30, 2016, and October 20, 2016
- Published electronically: May 4, 2017
- Communicated by: Nimish A. Shah
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4141-4149
- MSC (2010): Primary 20F69, 05C50; Secondary 20E08, 30F40
- DOI: https://doi.org/10.1090/proc/13568
- MathSciNet review: 3690601