A structural classification theorem in modular representation theory: for a fixed prime p, it determines all finite groups G that possess exactly two irreducible p-Brauer characters of degree larger than one. Because the p-core O_p(G) is contained in the kernel of every irreducible p-Brauer character, the problem reduces to the case O_p(G)=1, and the theorem gives an explicit list of the possible groups. It completes a classical program on groups with few nonlinear Brauer characters (Seitz; Dolfi-Navarro for one such character; Palfy's 1981 treatment of the two-character case for p'-groups), removing the earlier restriction to groups of order prime to p. The semilinear groups Gamma(l^n) over finite fields occur among the classified examples.
For a prime p, classifies all finite groups having exactly two irreducible p-Brauer characters of degree greater than one (two nonlinear irreducible p-Brauer characters). This completes a classical l…