A Family of Nonnormal Cayley Digraphs

We call a Cayley digraph Γ=Cay(G, S) normal for G if G_R, the right regular representationof G, is a normal subgroup of the full automorphism group Aut(Γ) of Γ. In this paper we determinethe normality of Cayley digraphs of valency 2 on nonabelian groups of order 2p~2 (p odd prime). As aresult, a fam...

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Published inActa mathematica Sinica. English series Vol. 17; no. 1; pp. 147 - 152
Main Authors Feng, Yan Quan, Wang, Dian Jun, Chen, Jing Lin
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 2001
Subjects
Algebraic group theory
Cayley
digraph
digraph;Normal
Mathematical analysis
Mathematics
Studies
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Summary:We call a Cayley digraph Γ=Cay(G, S) normal for G if G_R, the right regular representationof G, is a normal subgroup of the full automorphism group Aut(Γ) of Γ. In this paper we determinethe normality of Cayley digraphs of valency 2 on nonabelian groups of order 2p~2 (p odd prime). As aresult, a family of nonnormal Cayley digraphs is found.
Bibliography:Cayley digraph;Normal Cayley digraph
We call a Cayley digraph Γ=Cay(G, S) normal for G if G_R, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ) of Γ. In this paper we determine the normality of Cayley digraphs of valency 2 on nonabelian groups of order 2p~2 (p odd prime). As a result, a family of nonnormal Cayley digraphs is found.
11-2039/O1
Yan Quan FENG;Dian Jun WANG;Jing Lin CHEN Department of Mathematics, Northern JiaoTong University, Beijing 100044, P. R. China Department of Mathematics, Tsinghua University, Beijing 100084, P. R. China Department of Mathematics, Tangshan Normal College. Tangshan 063000, P. R. China
ISSN:1439-8516
1439-7617
DOI:10.1007/s101140000097