Cartan matrices for blocks of finite p-solvable groups with two simple modules
Let p be a prime, G a finite p-solvable group and B a p-block of G with exactly two simple modules M and N in characteristic p. The authors describe the Cartan matrix C of B in terms of its elementary divisors and of the dimensions of M and N. They are led to conjecture that the \(p'\)- parts of dim M and dim N coincide. This conjecture is proved in several cases. If the conjecture is true then C is determined by its elementary divisors and the orders of the vertices of M and N alone.
scientific article; zbMATH DE number 4212295
scientific article