9 problems

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

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…

Irreducibility conjecture. If $G$ is a finite simple group, then $R_2(G,s)$ is irreducible in $\mathcal{R}$. The examples in the paper show irreducibility for particular finite sim…