The class of acylindrically hyperbolic groups with uniform exponential growth is closed under geometric small cancellation quotients, implying a group with uniform growth but arbitrarily large torsion balls and universal lower bounds on growth rates for C''(λ) groups.
Short positive loxodromics in graph products
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abstract
We give a method for effectively generating generalised loxodromics in subgroups of graph products, using positive words. This has several consequences for the growth of subsets of these groups. In particular, we show that graph products of groups with strong product set growth properties also share those properties. We additionally show that the set of growth rates of a class of subgroups of any graph product of equationally noetherian groups is well-ordered.
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2024 1verdicts
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Uniform growth in small cancellation groups
The class of acylindrically hyperbolic groups with uniform exponential growth is closed under geometric small cancellation quotients, implying a group with uniform growth but arbitrarily large torsion balls and universal lower bounds on growth rates for C''(λ) groups.