Low-genus primitive monodromy groups with a nonunique minimal normal subgroup

Spencer Gerhardt; Eilidh McKemmie; Danny Neftin

doi:10.1080/00927872.2025.2564756

Low-genus primitive monodromy groups with a nonunique minimal normal subgroup

Spencer Gerhardt
, Eilidh McKemmie
, Danny Neftin

Mathematics

University of Southern California
Technion-Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Let X be a Riemann surface, and let (Formula presented.) be an indecomposable (branched) covering of genus g and degree n whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when (Formula presented.). Moreover, for arbitrary g, there are no such coverings with (Formula presented.) sufficiently large.

Original language	English
Pages (from-to)	1698-1707
Number of pages	10
Journal	Communications in Algebra
Volume	54
Issue number	4
DOIs	https://doi.org/10.1080/00927872.2025.2564756
State	Published - 2026

Keywords

Covering
Riemann surface
monodromy
primitive permutation group

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10.1080/00927872.2025.2564756

Cite this

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abstract = "Let X be a Riemann surface, and let (Formula presented.) be an indecomposable (branched) covering of genus g and degree n whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when (Formula presented.). Moreover, for arbitrary g, there are no such coverings with (Formula presented.) sufficiently large.",

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AU - McKemmie, Eilidh

AU - Neftin, Danny

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N2 - Let X be a Riemann surface, and let (Formula presented.) be an indecomposable (branched) covering of genus g and degree n whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when (Formula presented.). Moreover, for arbitrary g, there are no such coverings with (Formula presented.) sufficiently large.

AB - Let X be a Riemann surface, and let (Formula presented.) be an indecomposable (branched) covering of genus g and degree n whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when (Formula presented.). Moreover, for arbitrary g, there are no such coverings with (Formula presented.) sufficiently large.

KW - Covering

KW - Riemann surface

KW - monodromy

KW - primitive permutation group

UR - https://www.scopus.com/pages/publications/105018818168

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M3 - Article

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Low-genus primitive monodromy groups with a nonunique minimal normal subgroup

Abstract

Keywords

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