3 problems

Let $p$ be a prime. The coclass of a finite $p$-group is $n-c$, where $p^n$ is the order of the group and $c$ is the length of its lower central series. A coclass family is one of…

Let a coclass family be one of the finitely many families of finite $p$-groups of a given coclass, described by a parametrised presentation. Eick–Green conjecture. Cohomology is co…

Let $p$ be a prime, and let $m$ be a fixed non-negative integer. The coclass of a finite $p$-group $G$ of order $p^n$ and nilpotency class $c$ is $m=n-c$. Carlson's conjecture. The…