2 problems

NIP group conjecture. If $\mathscr{M}$ is $\aleph_0$-categorical and NIP, then $\mathscr{M}$ interprets an infinite group if and only if $\mathscr{M}$ trace defines an infinite gro…

NIP conjecture for omega-categorical groups. Every $\omega$-categorical group with NIP is nilpotent-by-finite.