Geodesic
Classification of regular balanced Cayley maps of minimal non-abelian metacyclic groups
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 433-443.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

In this paper, we classify the regular balanced Cayley maps of minimal non-abelian metacyclic groups. Besides the quaternion group Q8, there are two infinite families of such groups which are denoted by Mp, q(m, r) and Mp(n, m), respectively. Firstly, we prove that there are regular balanced Cayley maps of Mp, q(m, r) if and only if q = 2 and we list all of them up to isomorphism. Secondly, we prove that there are regular balanced Cayley maps of Mp(n, m) if and only if p = 2 and n = m or n = m + 1 and there is exactly one such map up to isomorphism in either case. Finally, as a corollary, we prove that any metacyclic p-group for odd prime number p does not have regular balanced Cayley maps.
DOI : 10.26493/1855-3974.1043.9d5
Keywords: Regular balanced Cayley map, minimal non-abelian group, metacyclic group 
@article{10_26493_1855_3974_1043_9d5,
     author = {Kai Yuan and Yan Wang and Hai-Peng Qu},
     title = {Classification of regular balanced {Cayley} maps  of  minimal non-abelian metacyclic groups},
     journal = {Ars Mathematica Contemporanea},
     pages = {433--443},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2018},
     doi = {10.26493/1855-3974.1043.9d5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1043.9d5/}
}
TY  - JOUR
AU  - Kai Yuan
AU  - Yan Wang
AU  - Hai-Peng Qu
TI  - Classification of regular balanced Cayley maps  of  minimal non-abelian metacyclic groups
JO  - Ars Mathematica Contemporanea
PY  - 2018
SP  - 433
EP  - 443
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1043.9d5/
DO  - 10.26493/1855-3974.1043.9d5
LA  - en
ID  - 10_26493_1855_3974_1043_9d5
ER  - 
%0 Journal Article
%A Kai Yuan
%A Yan Wang
%A Hai-Peng Qu
%T Classification of regular balanced Cayley maps  of  minimal non-abelian metacyclic groups
%J Ars Mathematica Contemporanea
%D 2018
%P 433-443
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1043.9d5/
%R 10.26493/1855-3974.1043.9d5
%G en
%F 10_26493_1855_3974_1043_9d5
Kai Yuan; Yan Wang; Hai-Peng Qu. Classification of regular balanced Cayley maps  of  minimal non-abelian metacyclic groups. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 433-443. doi : 10.26493/1855-3974.1043.9d5. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1043.9d5/

Cité par Sources :