5 problems

Let $S$ be any surface of finite type, and let $g_1,\dots,g_l\in MCG(S)$. For a subset $A$ of a group, write $\langle\langle A\rangle\rangle$ for its normal closure. Dehn-filling c…

Let $S$ be a finite-type surface, let $\mathcal{MCG}(S)$ be its mapping class group, and let $\mathcal{B}=\{\phi_1,\dots,\phi_k\}$ be a collection of elements. For a positive integ…

Positive-relator quotient conjecture.

Let $B_n$ be the braid group on $n$ strands, and let $\Sigma_n$ denote the finite quotient under consideration. A finite quotient is non-cyclic if it is not a cyclic group. Margali…

Let $G$ be a finite group, let $Z(G)$ denote its center, and call $G$ induced regular when the induced non-centralizer graph on $G\setminus Z(G)$ is regular. A finite group is an e…