3 problems

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

Suppose $G$ is a group and $\mathscr{O}$ is an $N_\infty$ operad: a $G$-operad whose spaces are $a3$-free, whose fixed-point subspaces are empty or contractible, and which has fixe…