Relativization of symmetries on quandles

Yuki Imamura; Tomoki Yoshida

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arXiv · 2607.02204

Relativization of symmetries on quandles

Yuki Imamura·Tomoki Yoshida

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Abstract

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.

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BibTeX RIS

Yuki Imamura, Tomoki Yoshida. 2026-09-12. Relativization of symmetries on quandles. https://arxiv.org/abs/2607.02204

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