6 problems

Let $\ell$ be a positive integer. Theorem, Corollary and Corollary are the results established earlier in the paper for the corresponding construction, with $\ell$ bounded by $8$.…

Let $K$ be a quadratic field, and let $G=\operatorname{Gal}(\mathrm{F}_3^2(K)\mid K)$ be its second $3$-class group. The TKT a.1 defect-zero exclusion conjecture. The transfer kern…

Let $p$ be a prime, let $k$ be a field of characteristic $p$, and let $(G_i \mid i \geq 0)$ be a coclass family of finite $p$-groups. Cohomology stabilization conjecture. There exi…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. Let $\mathcal T$ be a maximal coclass tree in $\mathcal G_{r,K}$ with maximal infinite path $A_1\to A_2\to\cdots$. Write…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. For an algebra $A$ in $\mathcal G_{r,K}$, write $\mathcal T(A)$ for the rooted subgraph consisting of all paths starting at…

Let $r\in\mathbb N_0$ and let $K$ be an arbitrary field. The graph $\mathcal G_{r,K}$ has rooted-tree components, and a maximal infinite path is an infinite path starting at the ro…