9 problems

For finite groups $H_1,H_2$, write $H_1\implies H_2$ when every finite group having a quotient isomorphic to $H_1$ also has a subgroup isomorphic to $H_2$. The symmetric-group quot…

Analytic continuation conjecture. The function $\zeta_{\mathrm{ts}}(s;G,H)$ admits an analytic continuation to the complex plane, with poles reflecting the arithmetic structure of…

Modular distribution of invariants. The invariants of topo-symmetric extensions are distributed uniformly modulo $\gcd(|G|,|H|)$ in the sense above. Numerical experiments for small…

Compatible normal series conjecture. Two groups are compatible if and only if they have compatible normal series.

Let $\calf$ be a saturated fusion system over a $p$-group $S$ such that $O_p(\calf)=1$. Set $\cale=F^*(\calf)$, a fusion subsystem over $T\nsg S$, and let $\call$ be a centric link…

Let $\left(\Sigma\times G,\sigma\rtimes\Psi\right)$ be an irreducible group-extended Markov system with finite alphabet $I$, and let $\varphi:\Sigma\rightarrow\mathbb{R}$ be a Höld…

Let $(\widetilde{G^*},A^*,G^*)$ be in Situation $(0)$, and let $B$ be the parameter set used to define the connected components. Suppose … Let $H$ be a $B$-invariant subgroup of…

Connected-component inclusion conjecture. Then

Let $C_n$ be a cyclic group of order $n$ and let $L$ be a finite-rank integral lattice. For a split group extension … let $\{E_*,d_*\}$ denote its Lyndon–Hochschild–Serre spectral…