Linear criteria for lifting automorphisms of elementary abelian regular coverings
نویسندگان
چکیده
For a given finite connected graph , a group H of automorphisms of and a finite group A, a natural question can be raised as follows: Find all the connected regular coverings of having A as its covering transformation group, on which each automorphism in H can be lifted. In this paper, we investigate the regular coverings with A = Zp , an elementary abelian group and get some new matrix-theoretical characterizations for an automorphism of the base graph to be lifted. As one of its applications, we classify all the connected regular covering graphs of the Petersen graph satisfying the following two properties: (1) the covering transformation group is isomorphic to the elementary abelian p-group Zp , and (2) the group of fibre-preserving automorphisms of a covering graph acts arc-transitively. As a byproduct, some new 2and 3-arc-transitive graphs are constructed. © 2003 Elsevier Inc. All rights reserved. AMS classification: Primary 05C50, 05C75
منابع مشابه
Elementary Abelian Covers of Graphs
Let CG (X ) be the set of all (equivalence classes of) regular covering projections of a given connected graph X along which a given group G ≤ Aut X of automorphisms lifts. There is a natural lattice structure on CG (X ), where ℘1 ≤ ℘2 whenever ℘2 factors through ℘1. The sublattice CG (℘) of coverings which are below a given covering ℘ : X̃ → X naturally corresponds to a lattice NG (℘) of certai...
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملGroup Actions, Coverings and Lifts of Automorphisms Group Actions, Coverings and Lifts of Automorphisms
a Supported in part by \Ministrstvo za znanost in tehnologijo Slovenije", proj.no. Abstract The problem of lifting automorphisms of a (fairly arbitrary) topological space to automorphisms of a covering space is studied by means of voltage groups. To this end we introduce some required background results regarding group actions and covering spaces.
متن کاملALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS
Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...
متن کاملSome properties of marginal automorphisms of groups
AbstractLet W be a non-empty subset of a free group. The automorphism of a group G is said to be a marginal automorphism, if for all x in G,x^−1alpha(x) in W^*(G), where W^*(G) is the marginal subgroup of G.In this paper, we give necessary and sufficient condition for a purelynon-abelian p-group G, such that the set of all marginal automorphismsof G forms an elementary abelian p-group.
متن کامل