6 problems

Let $p$ be a prime greater than $7$, let $G=PGL_2(p)$, and let $\Omega$ be the permutation domain of the action under consideration. The relational-complexity conjecture asserts th…

Let $q$ be a prime power, and let $\operatorname{PSL}(2,q)$ act on the $2$-subsets of the projective line $\operatorname{PG}(1,q)$. Recall that the group has the Erdős–Ko–Rado (EKR…

Let $\alpha$, $\beta$, and $\gamma$ be the three generators constructed from the elements in the preceding construction, and let $\langle\alpha,\beta,\gamma\rangle$ denote the subg…

Let $G\cong PSL(2,q)$ with $q=p^d$ and $d>1$. A chiral polytope existence conjecture asserts that $G$ is the automorphism group of a chiral polytope of rank $4$ if and only if one…

Let $G=\mathrm{PSL}(2,p)$), and let $\iota_n(G)$ denote the set of divisors occurring as the relevant invariant for irredundant generating sequences of length $n$ in the paper. Fou…

Let $q$ be an odd square prime power. Let $L_2(q)$ be the simple projective special linear group, and let $b$ and $c$ be the outer automorphisms described above, with…