内交换亚循环群上的正则凯莱地图
发布时间：2018-12-15 17:54
【摘要】：本文主要研究有限群论在地图中的作用.我们分类了有限内交换亚循环群上的中心对称正则凯莱地图.另外,作为群作用的另一个表现,我们探究了一类p群Mp(2,1)上的skew-morphism.有限内交换亚循环群在同构意义下共有三类：第一类是四元数群Q8,第二类和第三类我们在本文中分别用Mp,q(m,r)和Mp(n,m)标记,它们的定义请参见正文.在本论文中,我们研究的第一个问题是分类内交换亚循环的中心对称正则凯莱地图.四元数群Q8上的中心对称正则凯莱地图在其它文献中已经被考虑了,因此我们不再考虑这个群.第二类内交换亚循环群Mp,q(m,r)同时也是内循环群,我们证明了这类群只有当q=2即Mp,2(m,r)上存在中心对称正则凯莱地图.设p-1=2es,(s,2)=1,当m≥2时,群Mp,2(m,r)上存在s个互不同构的中心对称正则凯莱地图.而第三类内交换亚循环群Mp(n,m)是一类p群,我们证明了只有当p=2而且m=n或者n=m+1时,即只有群M2(n,n)和M2(n+1,n)上存在中心对称正则凯莱地图.在同构意义下,它们皆只有一个4度中心对称正则凯莱地图.我们研究的第二个问题是讨论p群上skewv-同态的存在性.一个有限群G上存在正则凯莱地图当且仅当G存在满足一定条件的skew-同态.因此研究有限群的skew-同态也是地图理论的一部分重要内容.在本文中,我们证明了Mp(2,1)不存在p2阶skew-morphism.
[Abstract]:This paper focuses on the role of finite group theory in maps. We classify the centrosymmetric canonical Calais maps on finite inner commutative subcyclic groups. In addition, as another representation of group action, we investigate the skew-morphism. on a class of p-group Mp (2t1). There are three classes of finite inner commutative subcyclic groups in the sense of isomorphism: the first is a quaternion group Q8, the second and the third are marked by Mp,q (MKR) and Mp (NM) in this paper, respectively. For their definitions, please refer to the text. In this paper, the first problem we study is the centrosymmetric canonical Calais map of commutative subcycles within the classification. The centrosymmetric canonical Calais map on quaternion group Q8 has been considered in other literatures, so we do not consider this group. The second kind of inner commutative subcyclic group Mp,q (MKR) is also an inner cyclic group. We prove that only if Q2, that is Mp,2 (MKR), there exists a centrosymmetric regular Calais map. Let p-1m2es, (sb2) = 1. when m 鈮，
本文编号：2381058
[Abstract]:This paper focuses on the role of finite group theory in maps. We classify the centrosymmetric canonical Calais maps on finite inner commutative subcyclic groups. In addition, as another representation of group action, we investigate the skew-morphism. on a class of p-group Mp (2t1). There are three classes of finite inner commutative subcyclic groups in the sense of isomorphism: the first is a quaternion group Q8, the second and the third are marked by Mp,q (MKR) and Mp (NM) in this paper, respectively. For their definitions, please refer to the text. In this paper, the first problem we study is the centrosymmetric canonical Calais map of commutative subcycles within the classification. The centrosymmetric canonical Calais map on quaternion group Q8 has been considered in other literatures, so we do not consider this group. The second kind of inner commutative subcyclic group Mp,q (MKR) is also an inner cyclic group. We prove that only if Q2, that is Mp,2 (MKR), there exists a centrosymmetric regular Calais map. Let p-1m2es, (sb2) = 1. when m 鈮，
本文编号：2381058
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