On the automorphism group of a tree
Copyright policy )On the automorphism group of a tree
AbstractIt is shown that H = Γ(T)v is normal in G = Γ(Tv) for any tree T and any vertex v, if and only if, for all vertices u in the neighborhood N of v, the set of images of u under G is either contained in N or has precisely the vertex u in common with N and every vertex in the set of images is fixed by H. Further, if S is the smallest normal subgroup of G containing H then GS is the direct product of the wreath products of various symmetric groups around groups of order 1 or 2. The degrees of the symmetric groups involved depend on the numbers of isomorphic components of Tv and the structure of such components.
Computational Theory and Mathematics, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Discrete Mathematics and Combinatorics, Graphs and abstract algebra (groups, rings, fields, etc.), Trees, Theoretical Computer Science
Computational Theory and Mathematics, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Discrete Mathematics and Combinatorics, Graphs and abstract algebra (groups, rings, fields, etc.), Trees, Theoretical Computer Science
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