Submodules of indecomposable modules in blocks with cyclic defect group (Q1083525)

Let F be a field of prime characteristic, let G be a finite group, and let B be a block of FG with cyclic defect group. Then B has only finitely many indecomposable modules. The authors prove that all Loewy layers of all indecomposable B-modules are multiplicity free. Every (non- projective) indecomposable B-module W can be described (up to isomorphism) by a certain ''zig-zag diagram'' D(W) whose nodes represent the composition factors of W. The authors show that for any submodule U of W, D(U) is obtained from D(W) by successively removing nodes from the top of D(W). Another submodule U' of W is isomorphic to U if and only if W/U' is isomorphic to W/U.