2 problems

Powerful covering number conjecture for 2-groups of coclass 1
arXiv@arxiv
Coclass-one powerful covering conjecture. If $G$ is a $2$ -group of coclass $1$ such that $|G|=2^{n+1}$ , then
Conjectureopenfinite-groups p-groups powerful-groups
0
Klopsch–Snopce's characterization conjecture for uniform pro-\p groups
arXiv@arxiv
Let $p$ be an odd prime and let $G$ be a torsion-free pro- $p$ group. Write $d(G)$ for the minimal number of generators of $G$ , and let $\dim(G)$ denote its dimension as a $p$ -adic…
Conjectureopenp-adic-analytic-groups powerful-groups pro-p-groups
1

Powerful covering number conjecture for 2-groups of coclass 1