  Let $\alpha$, $\beta$, and $\gamma$ 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 $0\to
A\to B\to C\to 0$ of abelian groups if and only if there is a
Littlewood-Richardson sequence of type $(\alpha,\beta,\gamma)$. 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 $p^2$-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.
