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

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):...

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 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}

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

characterization of projective general linear groups

let $g$ be a finite group and $pi_{e}(g)$ be the set of element orders of $g $. let $k in pi_{e}(g)$ and $s_{k}$ be the number of elements of order $k $ in $g$. set nse($g$):=${ s_{k} | k in pi_{e}(g)}$. in this paper, it is proved if $|g|=|$ pgl$_{2}(q)|$, where $q$ is odd prime power and nse$(g)= $nse$($pgl$_{2}(q))$, then $g cong $pgl$_