Cyclically presented groups with length four positive relators

2016/11/16 by Bogley, William A., Parker, Forrest W.
#20E36 #20F05 (Primary) #57M20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1611.05496

Abstract

For cyclically presented groups G = G_n(w) with positive length four relators w = x₀x_jx_kx_l in the free group with basis x₀, x₁, …, x_n-1, we classify finiteness and, modulo two unresolved cases, we classify asphericity for the underlying presentations. We show that the fixed point subgroup of the shift x_i ↦ x_i+1 is always finite and we relate finiteness of G and asphericity to the dynamics of the shift action by the cyclic group of order n on the nonidentity elements of G.

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