From Littlewood-richardson Sequences to Subgroup Embeddings and Back

Abstract. Let α, β, and γ be partitions describing the isomorphism types of the finite abelian p-groups A, B, and C. From theorems by Green and Klein it is well-known that there is a short exact sequence 0→ A→ B → C → 0 of abelian groups if and only if there is a Littlewood-Richardson sequence of type (α, β, γ). Starting from the observation that a sequence of partitions has the LR property if and only if every subsequence of length 2 does, we demonstrate how LR-sequences of length two correspond to embeddings of a p-bounded subgroup in a finite abelian p-group. Using the known classification of all such embeddings we derive short proofs of the theorems by Green and Klein.