Some remarks on symmetrical extensions of graphs

详细信息    查看全文

• 作者：V. I. Trofimov
• 关键词：graph ; automorphism group ; symmetrical extension of graphs
• 刊名：Proceedings of the Steklov Institute of Mathematics
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：289
• 期：1-supp
• 页码：199-208
• 全文大小：424 KB
• 参考文献：1.V. I. Trofimov, 鈥淭he finiteness of the number of symmetrical 2-extensions of the d-dimensional grid and similar graphs,鈥?Proc. Steklov Inst. Math. 285(Suppl. 1), S169鈥揝182 (2014).MATH MathSciNet View Article
  2.E. A. Neganova and V. I. Trofimov, 鈥淪ymmetrical extensions of graphs,鈥?Izv. Math. 78(4), 809鈥?35 (2014).MATH MathSciNet View Article
  3.M. Hall, 鈥淎 topology for free groups and related topics,鈥?Ann. Math. 52, 127鈥?39 (1950).View Article
  4. International Tables for Crystallography. Vol. A: Space-Group Symmetry, Ed. by Th. Hahn (Springer, Dordrecht, 2005).
  
• 作者单位：V. I. Trofimov (1) (2)
  
  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia
  2. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8605

文摘

It is proved that results from a previous paper of the author on symmetrical 2-extensions of graphs can be extended to symmetrical p-extensions of graphs for any prime p. In particular, it is proved that, for any prime p, there are only finitely many symmetrical p-extensions of a locally finite graph with an abelian subgroup of finite index in its automorphism group. Some refinements of these results are also obtained. In addition, we consider the question on the possibility to represent symmetrical extensions of a d-dimensional grid (and similar graphs) in the d-dimensional affine Euclidean space in such a way that a corresponding vertex-transitive group of automorphisms of the extension is induced by some crystallographic group of motions of the space.