On exponential growth and uniformly exponential growth for groups

By John S. Wilson. 2004

121 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c7743210a4be923014f63acbc981d2689987b2b

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the joint spectral radius for isometries of non-positively curved spaces and uniform growth (2018, unknown): “ a non-abelian free subgroup ? Note that it is certainly true for discrete subgroups of isometries of a tree, because they are virtually free [4]. Note further that according to a result of J. Wilson [73] the question has a negative answer, if we drop the assumption that xes no point on the tree (or”
Groups St Andrews 2005: Self-similarity and branching in group theory (2007, background): “Branch groups also played a role in the construction of groups with non-uniform exponential growth, answering a question of Gromov [9].”
Groups acting on manifolds: around the Zimmer program (2008, background): “linear groups, exponential growth implies exponential growth by a theorem of Eskin, Mozes and Oh [50]. There are examples of groups having exponential but not uniform exponential growth due to Wilson [230]. This raises the following question. Question 13.5. Let M be a compact manifold and Γ a ﬁnitel”
Classification of groups generated by 3-state automata over a 2-letter alphabet (2008, background): “... series [BG00b] (answering a question of E. Zelmanov on classification of groups of finite width), branch properties [Gri84, Neu86, Gri00] (answering some questions of S. Pride and M. Edjvet [Pri80, EP84]), finiteness of the index of maximal subgroups and presence or absence of the congruence pro”
On amenability of automata groups (2008, background): “ions of “largeness” formulated by Edjvet and Pride, and more recently by the ﬁrst author [Bar03] to construct groups of exponential word growth for which the inﬁmum of the growth rates is 1 (also see [Wil04]). All of these groups are subgroups of BA. 2. Bounded automata In this Section we recall som”
Probability on Trees and Networks (2017, background): “This is part of the field called proper scoring rules; see Winkler (1969) and Gneiting and Raftery (2007).”
Uniform Uniform Exponential Growth of Subgroups of the Mapping Class Group (2008, background): “Exponential growth does not generally imply uniform exponential growth [ W ], but Eskin, Mozes, and Oh proved this implication holds for linear groups over a field with characteristic zero [EMO].”