Further restrictions on the structure of finite DCI-groups: an addendum

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• 作者：Edward Dobson ; Joy Morris ; Pablo Spiga
• 关键词：Cayley graph ; Isomorphism problem ; CI ; group ; Dihedral group ; 20B10 ; 20B25 ; 05E18
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：42
• 期：4
• 页码：959-969
• 全文大小：423 KB
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• 作者单位：Edward Dobson (1) (2)
  Joy Morris (3)
  Pablo Spiga (4)
  
  1. Department of Mathematics and Statistics, Mississippi State University, PO Drawer MA, Mississippi State, MS, 39762, USA
  2. IAM, University of Primorska, 6000, Koper, Slovenia
  3. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada
  4. Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Via Cozzi 55, 20125, Milan, MI, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Convex and Discrete Geometry
  Order, Lattices and Ordered Algebraic Structures
  Computer Science, general
  Group Theory and Generalizations
  
• 出版者：Springer U.S.
• ISSN：1572-9192

文摘

A finite group R is a \({\mathrm {DCI}}\)-group if, whenever S and T are subsets of R with the Cayley digraphs \({\mathrm {Cay}}(R,S)\) and \({\mathrm {Cay}}(R,T)\) isomorphic, there exists an automorphism \(\varphi \) of R with \(S^\varphi =T\). The classification of \({\mathrm {DCI}}\)-groups is an open problem in the theory of Cayley digraphs and is closely related to the isomorphism problem for digraphs. This paper is a contribution toward this classification, as we show that every dihedral group of order 6p, with \(p\ge 5\) prime, is a \({\mathrm {DCI}}\)-group. This corrects and completes the proof of Li et al. (J Algebr Comb 26:161-81, 2007, Theorem 1.1) as observed by the reviewer (Conder in Math review MR2335710). Keywords Cayley graph Isomorphism problem CI-group Dihedral group