On Recognition by Order and Degree Pattern of Finite Simple Groups

Let GK(G) be the prime graph associated with a finite group G and D (G) be the degree pattern of G. A finite group G is said to be k-fold OD-characterizable if there exist exactly k non-isomorphic groups H such that vertical bar H vertical bar = vertical bar G vertical bar and D (H) = D (G). A 1-fold OD-characterizable group is simply called OD-characterizable. The purpose of this paper is twofold. First, it lists a number of such simple groups that have been already investigated. Second, it shows that the simple groups L 6(3) and U 4(5) are OD-characterizable, too.