ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.)
ARS MATHEMATICA CONTEMPORANEA 23 (2023) #P2.03
https://doi.org/10.26493/1855-3974.2415.fd1
(Also available at http://amc-journal.eu)
Classification of minimal Frobenius hypermaps*
Kai Yuan , Yan Wang †
School of Mathematics and Information Science, Yan Tai University, Yan Tai, P.R.C.
Received 23 August 2020, accepted 24 May 2022, published online 11 November 2022
Abstract
In this paper, we give a classification of orientably regular hypermaps with an automor-
phism group that is a minimal Frobenius group. A Frobenius group G is called minimal if
it has no nontrivial normal subgroup N such that G/N is a Frobenius group. An orientably
regular hypermap H is called a Frobenius hypermap if Aut(H) acting on the hyperfaces
is a Frobenius group. A minimal Frobenius hypermap is a Frobenius hypermap whose
automorphism group is a minimal Frobenius group with cyclic point stabilizers. Every
Frobenius hypermap covers a minimal Frobenius hypermap. The main theorem of this
paper generalizes the main result of Breda D’Azevedo and Fernandes in 2011.
Keywords: Frobenius hypermap, Frobenius group.
Math. Subj. Class. (2020): 57M15, 05C25, 20F05
*The Authors thank the referees for their helpful comments.
†Corresponding author. Supported by NSFC (No. 12101535) and NSFS (No. ZR2020MA044).
E-mail addresses: pktide@163.com (Kai Yuan), wang−yan@pku.org.cn (Yan Wang)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 1855-3966 (tiskana izd.), ISSN 1855-3974 (elektronska izd.)
ARS MATHEMATICA CONTEMPORANEA 23 (2023) #P2.03
https://doi.org/10.26493/1855-3974.2415.fd1
(Dostopno tudi na http://amc-journal.eu)
Klasifikacija minimalnih Frobeniusovih
hiperzemljevidov*
Kai Yuan , Yan Wang †
School of Mathematics and Information Science, Yan Tai University, Yan Tai, P.R.C.
Prejeto 23. avgusta 2020, sprejeto 24. maja 2022, objavljeno na spletu 11. novembra 2022
Povzetek
V tem članku podamo klasifikacijo orientabilno regularnih hiperzemljevidov, za katere
velja, da je njihova grupa avtomorfizmov minimalna Frobeniusova grupa. Frobeniusova
grupa G se imenuje minimalna, če nima nobene netrivialne edinke N , za katero bi bila
G/N Frobeniusova grupa. Orientabilno regularen hiperzemljevid H se imenuje Frobe-
niusov hiperzemljevid, če je grupa Aut(H), delujoča na hiperlicih, Frobeniusova grupa.
Minimalen Frobeniusov hiperzemljevid je Frobeniusov hiperzemljevid, katerega grupa av-
tomorfizmov je minimalna Frobeniusova grupa s cikličnimi stabilizatorji točk. Vsak Frobe-
niusov hiperzemljevid je krov nad minimalnim Frobeniusovim hiperzemljevidom. Glavni
izrek tega članka posplošuje glavni izrek Breda D’Azevede in Fernandesa iz leta 2011.
Ključne besede: Frobeniusov hiperzemljevid, Frobeniusova grupa.
Math. Subj. Class. (2020): 57M15, 05C25, 20F05
*Avtorja se zahvaljujeta recenzentom za njihove koristne pripombe.
†Kontaktni avtor. Podprt s strani NSFC (št. 12101535) in NSFS (št. ZR2020MA044).
E-poštna naslova: pktide@163.com (Kai Yuan), wang−yan@pku.org.cn (Yan Wang)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/