Permutation groups, their fundamental theory and applications are discussed in this
introductory book. It focuses on those groups that are most useful for studying symmetric …

The relative fixity of a digraph\(\Gamma\) is defined as the ratio between the largest number
of vertices fixed by a nontrivial automorphism of\(\Gamma\) and the number of vertices …

We consider a code to be a subset of the vertex set of a Hamming graph. In this setting a
neighbour of the code is a vertex which differs in exactly one entry from some codeword …

In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define
a decomposition of elements of the full monomial group and exploit this to describe …

We study locally $ s $-arc-transitive graphs arising from the quasiprimitive product action
(PA). We prove that, for any locally $(G, 2) $-arc-transitive graph with $ G $ acting …

We consider codes of length $ m $ over an alphabet of size $ q $ as subsets of the vertex set
of the Hamming graph $\Gamma= H (m, q) $. A code for which there exists an automorphism …

Before discussing the philosophy behind Question A, let us recall what a vertex-transitive
group of automorphisms is. A graph Γ is a pair (VΓ, EΓ) where EΓ is an asymmetric binary …

Group embedding into wreath products: Cartesian decomposition approach | Indian Journal of
Pure and Applied Mathematics Skip to main content Springer Nature Link Account Menu Find a …

The completely regular codes in Hamming graphs have a high degree of combinatorial
symmetry and have attracted a lot of interest since their introduction in 1973 by Delsarte …

Abstract We study (G, 2)-arc-transitive graphs for innately transitive permutation groups G
such that G can be embedded into a wreath product Sym Γ wr S ℓ acting in product action on …