From Littlewood-Richardson sequences to subgroup embeddings and back
| dc.creator | Schmidmeier, Markus | |
| dc.date | 2007-09-18 | |
| dc.date.accessioned | 2026-07-07T08:30:46Z | |
| dc.date.available | 2026-07-07T08:30:46Z | |
| dc.description | 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 $0\to A\to B\to C\to 0$ 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 $p^2$-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. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/0709.2920 | |
| dc.identifier | http://arxiv.org/abs/0709.2920 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138323 | |
| dc.subject | Group Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 5E05; 20E07 | |
| dc.title | From Littlewood-Richardson sequences to subgroup embeddings and back | |
| dc.type | text |