4 problems

Type-$\tilde{\mathfrak{Z}}$ conjecture. If $P(r,n,k,r-1,q)$ is perfect, then it is of type $\tilde{\mathfrak{Z}}$. The preceding theorem establishes the corresponding perfectness c…

Let $H(r,n,s)=P(r,n,r+1,s,1)$, where $P(r,n,k,s,q)$ is the cyclically presented group under consideration. Williams's conjecture. For integers $r,sgeq 1$ and $ngeq 2$ satisfying ……

Let $S^{TFFF}(n)$ and $S^{FFFF}(n)$ be the classes of cyclically presented groups defined in the source, and let $\Gamma_n(1,n/2-1)$ be the corresponding group. Exclusion conjectur…

Let $\Gamma_n(1,n/2-1)$ be the cyclically presented group in the source, let $\Gamma_n(1,n/2-1)^\mathrm{ab}$ denote its abelianisation, and let $d(G)$ be the minimum number of gene…