A Cayley graph for F2 × F2 which is not minimally almost convex
نویسندگان
چکیده
We give an example of a Cayley graph [Formula: see text] for the group which is not minimally almost convex (MAC). On other hand, standard does satisfy falsification by fellow traveler property (FFTP), strictly stronger. As result, any lying between FFTP and MAC (i.e., text]) dependent on generating set. This includes well-known properties convexity, were already known to depend set as well Poénaru’s condition basepoint loop shortening (LSP) dependence was previously unknown. also show that have LSP, so this depends
منابع مشابه
Thompson ’ s group F ( n ) is not minimally almost convex
We prove that Thompson’s group F (n) is not minimally almost convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for arbitrarily large values of m there exist elements g, h ∈ Bm such that dΓ(g, h) = 2 and dBm (g, h) = 2m. (Here Bm is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent eleme...
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متن کاملThompson ’ s group F ( n ) is not minimally almost convex Claire
We prove that Thompson’s group F (n) is not minimally almost convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for arbitrarily large values of m there exist elements g, h ∈ Bm such that dΓ(g, h) = 2 and dBm (g, h) = 2m. (Here Bm is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent eleme...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2021
ISSN: ['0218-1967', '1793-6500']
DOI: https://doi.org/10.1142/s0218196722500059