A generalization of the regularity of covering maps

Articles in Press

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

2 Department of Pure Mathematics, University of Gonabad, Gonabad, Iran

10.22034/as.2026.23085.1788

Abstract

We introduce $H$-regular covering spaces, a natural generalization of classical regular covers where normality in the whole fundamental group is replaced by invariance under conjugation by an arbitrary subgroup $H \le \pi_1(X,x_0)$. We give three equivalent characterizations of $H$-regularity and describe the deck transformation group via a normalizer quotient. When \(H=\pi_1(X,x_0)\), \(H\)-regularity reduces to the usual normality condition \(p_*\pi_1(\widetilde X,\tilde x)\trianglelefteq \pi_1(X,x_0)\); hence \(H\)-regular coverings are exactly ordinary regular coverings. In this case the \(H\)-orbit on each fiber is the whole fiber and the deck transformation group specializes to the classical quotient \(\operatorname{Cov}(\widetilde X/X)\cong \pi_1(X,x_0)/p_*\pi_1(\widetilde X,\tilde x)\).

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 25 September 2026

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