The decomposition numbers of the Rudvalis sporadic simple group and of its double covering group modulo 3 are completely determined. The results were obtained using the computer algebra system MOC developed by Jansen, Lux, Parker, and the author, but the proofs are given in conventional form and can be verified by hand with the ordinary character table.

Introduction. In this paper I study covering spaces in which the base space is an arbitrary topological space. No use is made of arcs and no assumptions of a global or local nature are required. In consequence, the fundamental group ir(X, Xo) which we obtain frequently reflects local properties which are missed by the usual arcwise group iri(X, Xo). We obtain a perfect Galois theory of covering...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

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-theoret...

Recently, a new parameter of a code, referred to as the remoteness, has been introduced.This parameter can be viewed as a dual to the covering radius. It is exactly determined for the cyclic and dihedral groups. In this paper, we consider the group $U_{6n}$ as a subgroup of $S_{2n+3}$ and obtain its remoteness.  We show that the remoteness of the permutation code $U_{6n}$ is $2n+2$.  Moreover, ...

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...