p-Steinberg Characters of Alternating and Projective Special Linear Groups

Irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$

‎‎Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

Characterization of some projective special linear groups in dimension four by their orders and degree patterns

‎Let $G$ be a finite group‎. ‎The degree pattern of $G$ denoted by‎ ‎$D(G)$ is defined as follows‎: ‎If $pi(G)={p_{1},p_{2},...,p_{k}}$ such that‎ ‎$p_{1}

Characterization of projective special linear groups in dimension three by their orders and degree patterns

The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):...

Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups

The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).

On the Restriction of Characters of Special Linear Groups of Dimension Three