Relativization of symmetries on quandles

@misc{imamura2026relativization,
  title = {{Relativization of symmetries on quandles}},
  author = {Yuki Imamura and Tomoki Yoshida},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.02204},
  eprint = {2607.02204},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.02204},
}

TY  - UNPB
TI  - Relativization of symmetries on quandles
AU  - Yuki Imamura
AU  - Tomoki Yoshida
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2607.02204
UR  - https://arxiv.org/abs/2607.02204
AB  - This paper introduces relative versions of the inner automorphism group and the transvection group associated with surjective quandle homomorphisms. By using the relative inner automorphism group, we define a notion of connectedness for surjective homomorphisms. We characterize connected homomorphisms algebraically as quotient maps, and use the relative transvection group to establish a maximal connected--covering factorization for arbitrary surjections. We also introduce strongly connected homomorphisms via the relative transvection group, and classify them in terms of perfect normal subgroups of inner automorphism groups. A later part of this paper studies surjective homomorphisms for which the relative inner automorphism group acts $2$-transitively on each fiber. Under this assumption, we classify the possible quandle structures of the finite fibers.
ER  -