Finite groups, modular representations and the Green correspondence

This thesis is mostly concerned with the block theory of finite groups whose 2-sylow subgroups are assumed to be elementary abelian of order 4. In chapter 3 indecomposable representations of the cyclic group of order 2 over a 2-adic ring of characteristic 0 are classified, and in chapter 4 this is used to describe the Green correspondence and the modular constitution of modules in 2-b1ocks of 0 of defect 1. Chapter 5 describes the decomposition matrix of the principal b1ock,and the Green correspondence is shown to be of a fairly simple form. The submodule lattices of projective indecomposable are discussed in chapter 6 and are used to determine the Loewy and composition factors of the kernels of a projective resolution of kG. The groups PSL(2,q),q =3,5(mod 8) satisfy the assumptions made about our group G, and in chapter 7 these groups are shown to satisfy our results. Some wider topics are discussed in chapter 8. The methods used in the body of the thesis are shown to be applicable outside the main class of groups considere