Regular Cayley maps for finite abelian groups
Regular Cayley maps for finite abelian groups
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DOI：
10.1007/s10801-006-0037-0
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发表时间：
2007-05
影响因子：
0.8
通讯作者：
M. Conder;R. Jajcay;T. Tucker
中科院分区：
文献类型：
--
作者：
M. Conder;R. Jajcay;T. Tucker
有限群A的正则Cayley映射是一个可定向映射，它的保向自同构群G正则地作用在有向边集上，并有一个与A同构的子群正则地作用在顶点集上.本文考虑了确定哪些交换群具有正则Cayley映射的问题。分析是纯代数的，涉及A的标准型的结构。A在G中正规的情形涉及到A的秩与A的自同构群的指数之间的关系，一般情形用Ito定理分析G =AY的分解，其中Y是顶点的（循环）稳定子.
A regular Cayley map for a finite groupAis an orientable map whose orientation-preserving automorphism groupGacts regularly on the directed edge set and has a subgroup isomorphic toAthat acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical form forA. The case whenAis normal inGinvolves the relationship between the rank ofAand the exponent of the automorphism group ofA, and the general case uses Ito's theorem to analyze the factorizationG=AY, whereYis the (cyclic) stabilizer of a vertex.