10 problems

Kuzmin's conjecture. The nilpotency degree satisfies

A Goursat germ is a germ of a Goursat distribution, and a tangential germ is one belonging to the tangential class. Mormul's Goursat conjecture. Goursat germs are strongly nilpoten…

Let a special $m$-flag germ have singularity class … Let $c^i_j$ denote the constants appearing in its EKR normal form. Strong nilpotency conjecture. The germ is strongly nilpotent…

Base-3 digit conjecture.

Base-7 digit conjecture.

Degree and nilpotence-index conjecture. The degree $D_{19}(k,5)$ is given by the displayed residue-class formulas in the source; moreover, $c_0=0$, $c_1=2$, and

Let $p>2$ be a prime, and let $h(p)$ be the minimal integer such that every Lie ring $L$ with a grading … by $(\mathbb{Z}_p,+)$ satisfying $L_{\overline{0}}=\\{0\\}$ is nilpotent o…

The Main Conjecture. The quotient $Q/N(Q)$ is an abelian group and $Q/Z(Q)$ is a group. In particular, $Q$ is nilpotent of class at most $3$.

Let ${\mathbb F}$ be a finite field and ${\mathbb L}$ an infinite field such that … Let $C_{n,d}^{\mathbb F}$ and $C_{n,d}^{\mathbb L}$ denote the nilpotency degrees of the relativ…

Let $A$ be an object with endomorphisms $\pi_1$ and $\pi_2$. Set … and … Assume also that … for all $i$ and $j$. Let $\nu$ be the hook partition occurring in the definition of the…