CHARACTERIZATION OF PROJECTIVE SPECIAL LINEAR GROUPS IN DIMENSION THREE BY THEIR ORDERS an‎d DEGREE PATTERNS

Abstract. The prime graph 􀀀(G) of a group G is a graph with vertex set (G), the set of primes dividing the order of G, and two distinct vertices p and q are adjacent by an edge written p q if there is an element in G of order pq. Let (G) = fp1; p2; :::; pkg. For p 2 (G), set deg(p) := jfq 2 (G)jp qgj, which is called the degree of p. We also set D(G) := (deg(p1); deg(p2); :::; deg(pk)), where p1 < p2 < :::