3 problems

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.

Let $H(r,n,s)$ be the generalized Fibonacci group … where $r,s\geq 1$, $n\geq 2$, and subscripts are taken modulo $n$. The group $G$ is perfect when $G^{\mathrm{ab}}=1$. Non-perfec…