We study complex projective plane curves with a given group of automorphisms. Let $G$ be simple primitive subgroup $\mathrm{PGL}(3, \mathbf{C})$, which is isomorphic to $\mathfrak{A}_{6}$, $\mathfrak{A}_{5}$ or $\mathrm{PSL}(2, \mathbf{F}_{7})$. obtain necessary and sufficient condition on $d$ for the existence nonsingular curve degree invariant under $G$. also an analogous problem integral cur...

We study simply connected Lie groups $G$ for which the hull-kernel topology of primitive ideal space $\text{Prim}(G)$ group $C^*$-algebra $C^*(G)$ is $T_1$, that is, finite subsets are closed. Thus, we prove AF-embeddable. To this end, show if solvable and its action on centre $[G, G]$ has at least one imaginary weight, then no nonempty quasi-compact open subsets. in addition locally compact wi...

Let $G$ be a transitive permutation group on finite set $\Omega$ and recall that base for is subset of with trivial pointwise stabiliser. The size $G$, denoted $b(G)$, the minimal base. If $b(G)=2$ then we can study Saxl graph $\Sigma(G)$ which has vertex two vertices are adjacent if they form This vertex-transitive graph, conjectured to connected diameter at most $2$ when primitive. In this pa...