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PreprintCC BY 4.0arXiv

Skew-product groups of finite abelian p-groups

  • Jiawei He
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Abstract

A skew-morphism of a finite group G is a permutation σ of G fixing the identity element such that there exists a function π: G→ℤ satisfying σ(xy)=σ(x)σπ(x)(y) for all x,y∈ G. For a given skew-morphism σ of G, the product of the left regular representation of G and the cyclic group ⟨σ⟩ forms a permutation group on G, called a skew-product group of G. Skew-product groups of finite elementary abelian p-groups were investigated in \cite{DLYZ}. In the present paper, we extend this study to all finite abelian p-groups.

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Cite

BibTeXRIS
BibTeX
@misc{he2026skewproduct,
  title = {{Skew-product groups of finite abelian $p$-groups}},
  author = {Jiawei He},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38250},
  eprint = {2609.38250},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38250},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Skew-product groups of finite abelian p-groups
AU  - Jiawei He
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38250
UR  - https://arxiv.org/abs/2609.38250
AB  - A skew-morphism of a finite group G is a permutation σ of G fixing the identity element such that there exists a function π: G→ℤ satisfying σ(xy)=σ(x)σ^π(x)(y) for all x,y∈ G. For a given skew-morphism σ of G, the product of the left regular representation of G and the cyclic group ⟨σ⟩ forms a permutation group on G, called a skew-product group of G. Skew-product groups of finite elementary abelian p-groups were investigated in \cite{DLYZ}. In the present paper, we extend this study to all finite abelian p-groups.
ER  -