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Decompositions of homomorphisms of abelian p-groups with p2-bounded target

  • Stanisław Kasjan
  • Justyna Kosakowska
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Abstract

Let p be a prime. We classify homomorphisms H:V1→ V2 between abelian p-groups that are direct sums of cyclic groups, under the assumption p2V2=0. We prove that every such homomorphism is isomorphic to a direct sum of finite indecomposable representations and that this decomposition is unique up to isomorphism and reordering of the summands.

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Cite

BibTeXRIS
BibTeX
@misc{kasjan2026decompositions,
  title = {{Decompositions of homomorphisms of abelian $p$-groups with $p^2$-bounded target}},
  author = {Stanisław Kasjan and Justyna Kosakowska},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05156},
  eprint = {2611.05156},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05156},
}
RIS
TY  - UNPB
TI  - Decompositions of homomorphisms of abelian p-groups with p^2-bounded target
AU  - Stanisław Kasjan
AU  - Justyna Kosakowska
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05156
UR  - https://arxiv.org/abs/2611.05156
AB  - Let p be a prime. We classify homomorphisms H:V_1→ V_2 between abelian p-groups that are direct sums of cyclic groups, under the assumption p^2V_2=0. We prove that every such homomorphism is isomorphic to a direct sum of finite indecomposable representations and that this decomposition is unique up to isomorphism and reordering of the summands.
ER  -