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

A finite group R is a DCI -group if, whenever S and T are subsets of R with the Cayley digraphs Cay ( R , S ) and Cay ( R , T ) isomorphic, there exists an automorphism φ of R with S φ = T . The classification of DCI -groups is an open problem in the theory of Cayley digraphs and is closely related...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2015-12, Vol.42 (4), p.959-969
Main Authors: Dobson, Edward, Morris, Joy, Spiga, Pablo
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
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Summary:A finite group R is a DCI -group if, whenever S and T are subsets of R with the Cayley digraphs Cay ( R , S ) and Cay ( R , T ) isomorphic, there exists an automorphism φ of R with S φ = T . The classification of 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 6 p , with p ≥ 5 prime, is a DCI -group. This corrects and completes the proof of Li et al. (J Algebr Comb 26:161–181, 2007 , Theorem 1.1) as observed by the reviewer (Conder in Math review MR2335710).
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-015-0612-3