9 problems

Shortest-path bisaturation conjecture. A shortest path between the trivial $G$-transfer system and the complete $G$-transfer system on a Hasse diagram will pass through as many bis…

Rubin's saturation conjecture. For every $n$ there exists some $f(n)$ such that, for any collection of distinct primes $p_1,\ldots,p_n\geqslant f(n)$ and any choice of…

Disklike characterization conjecture. The maximal compatible transfer system is

Abelianness conjecture for saturated groups. If $G$ is a saturated finite group, then $G$ is abelian.

Two-component LSP compatibility conjecture. Then $T$ is not LSP and is compatible with the transfer system generated by adding the edge $e\to G$ to $T$.

Let $G$ be a finite group. A pair of $G$-transfer systems is called compatible when it satisfies the compatibility conditions for a pairing of $N_{\infty}$-operads, and it is reali…

Let $n\geqslant 0$. A transfer system in $T(n)$ is maximally extendable if it has the maximal extension property described in the surrounding definitions, and let $\mathfrak{A}_m$…

Let $G = \operatorname{SL}_2(\mathbb{F}_p)$ with $p > 5$, $p \neq 11$, and $p \equiv \pm 3 \mod 8$. Fix an arbitrary transfer system $\mathcal{R}$ on $G$, and let…

Fix positive integers $r_1,\ldots,r_k$, and let $p_1,\ldots,p_k$ be distinct primes. A saturated transfer system on a finite group is a transfer system satisfying the two-out-of-th…