11 problems

Let $w(x_{1},x_{2})$ be a word in two variables, and let ${\operatorname{PSL}}_{2}({\mathbb{F}}_q)$ denote the projective special linear group over the finite field with $q$ elemen…

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 $W_{\lambda}$ be the object whose stabilizer under the relevant $\operatorname{PGL}(3)$ action is denoted by $\operatorname{stab}(W_{\lambda})$, let $B$ and $A_g$ be the matric…

Let $q$ be a prime power with $q\equiv 1\pmod{4}$, and let $\PSL(2,q)$ act on the projective line. A 2-intersecting set is a collection of permutations any two of which agree on at…

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…

Rank-three conjecture for $PGL(2,q)$. The maximum rank of a string C-group representation of $PGL(2,q)$ should be three except when $q=5$.

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 $G=\mathrm{PSL}(2,p)$, where $p$ is prime. An irredundant generating set is a generating set such that removing any one generator leaves a collection that no longer generates…

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…