论文标题
有价值的$ p $ - 图和常规$ p $ - 图
Orientably-Regular $p$-Maps and Regular $p$-Maps
论文作者
论文摘要
如果它具有Prime $ p $ -power Vertices，则称为{\ it $ p $ -map}。 如果所有定向保留的自动形态的$ g^+$的组$ g^+$（分别是自动形态的组$ g $）是可求解的；如果$ g^+$（resp。$ g $）包含普通的sylow $ p $ -subgroup，则称为{\ it正常}。 在本文中，将证明两种有效的规范$ p $ - 图和常规$ p $ - 图是可以解决的，除了少数情况下$ p \ in \ {2，3 \} $，它们是正常的。 此外，将对非正常$ p $图表进行表征，并将给出一些普通$ p $图的属性和构造。
A map is called a {\it $p$-map} if it has a prime $p$-power vertices. An orientably-regular (resp. A regular ) $p$-map is called {\it solvable} if the group $G^+$ of all orientation-preserving automorphisms (resp. the group $G$ of automorphisms) is solvable; and called {\it normal} if $G^+$ (resp. $G$) contains the normal Sylow $p$-subgroup. In this paper, it will be proved that both orientably-regular $p$-maps and regular $p$-maps are solvable and except for few cases that $p\in \{2, 3\}$, they are normal. Moreover, nonnormal $p$-maps will be characterized and some properties and constructions of normal $p$-maps will be given.
