Classification and enumeration of skew morphisms of skew-type four on cyclic $2$-groups

@misc{hu2026classification,
  title = {{Classification and enumeration of skew morphisms of skew-type four on cyclic $2$-groups}},
  author = {Kan Hu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17199},
  eprint = {2609.17199},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17199},
}

TY  - UNPB
TI  - Classification and enumeration of skew morphisms of skew-type four on cyclic $2$-groups
AU  - Kan Hu
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17199
UR  - https://arxiv.org/abs/2609.17199
AB  - A skew morphism on a finite group A is a permutation φ on A that fixes the identity element of A and for which there exists an integer-valued function π:A→ℤ_|φ| such that φ(xy)=φ(x)φ^π(x)(y) for all x,y∈ A. The kernel of φ is the subgroup Kerφ={x∈ A| π(x)=1}, and the index [A:Kerφ] is called the skew-type of φ. In this paper we construct, classify and enumerate the skew morphisms of skew-type four on cyclic $2$-groups. Our main results give explicit formulas for all such skew morphisms and closed-form expressions for their numbers.
ER  -