CHARACTERIZATION OF THE PROJECTIVE GENERAL LINEAR GROUPS PGL(2,q) BY THEIR ORDERS AND DEGREE PATTERNS

Abstract

Let G be a finite group and π(G) = {p1, p2,…,pk}. For p ∈ π(G), we put deg (p) := |{q ∈ π(G)|p ~ q}|, which is called the degree of p. We also define D(G) := ( deg (p1), deg (p2), …, deg (pk)), where p1 < p2 < ⋯ < pk, which is called the degree pattern of G. Using the classification of finite simple groups, we characterize the projective general linear group PGL(2,q)(q a prime power) by its order and degree pattern in the present paper.