9 problems

Noferini–Williams conjecture.

Mohamed–Williams conjecture. The group $G_n(x_0x_kx_l)$ is not isomorphic to

Sieradski classification conjecture. The Sieradski groups $S(2,n)$ are the only Gilbert–Howie groups that are LOG groups; equivalently, they are the only groups of Fibonacci type…

Gilbert–Howie-to-Sieradski conjecture. If a Gilbert–Howie group is a LOG group, then it is a Sieradski group.

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 $L_j$ denote the $j$th Lucas number, and let $\Gamma_{2^t}(1,2^{t-1}-1)$ be the cyclically presented group in the source. In the cases where $16\mid n$, write $n=2^t m$ with…

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…