Thompson's group $F$ is not SCY

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...

Thompson ’ S Group F Is Not Almost Convex

We show that Thompson’s group F does not satisfy Cannon’s almost convexity condition AC(n) for any integer n in the standard finite two generator presentation. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our ...

DES is not a Group

We prove that the set of DES permutations (encryption and decryption for each DES key) is not closed under functional composition. This implies that, in general, multiple DES-encryption is not equivalent to single DES-encryption, and that DES is not susceptible to a particular known-plaintext attack which requires, on average, 228 steps. We also show that the size of the subgroup generated by t...

Thompson ’ 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...

A new application of random matrices : Ext ( C ∗ red ( F 2 ) ) is not a group