arXiv 1402.43732014-02-18math.COmath.GR

对“有限DCI-群结构的进一步限制”一文的评论

A comment on: "Further restrictions on the structure of finite DCI-groups"

Edward Dobson, Joy Morris, Pablo Spiga

备注：: This paper corrects and completes the proof of Theorem 1.1 (C.H.Li,Z.P.Lu, P.Palfy, Further restrictions on the structure of finite CI-groups, J. Algebr. Comb. 26 (2007), 161-181) as observed in the maths review MR2335710

摘要：

一个有限群R是CI-群，如果当S和T是R的子集且Cayley图Cay（R，S）和Cay（R，T）同构时，存在R的一个自同构x使得S^x=T. CI-群的分类是Cayley图理论中的一个公开问题，它与图的同构问题密切相关。本文是对这一分类的贡献，因为我们证明了每一个二面体群的阶为6p，其中p>3素数，是CI-群。

英文摘要：

A finite group R is a CI-group if, whenever S and T are subsets of R with the Cayley graphs Cay(R,S) and Cay(R,T) isomorphic, there exists an automorphism x of R with S^x=T. The classification of CI-groups is an open problem in the theory of Cayley graphs and is closely related to the isomorphism problem for graphs. This paper is a contribution towards this classification, as we show that every dihedral group of order 6p, with p>3 prime, is a CI-group.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。