Regular Maps Constructed from Linear Groups

TRANSITIVE t - DESIGNS AND STRONGLY REGULAR GRAPHS CONSTRUCTED FROM LINEAR GROUPS L ( 2 , q ) , q ≤ 23

In this paper we construct transitive t-designs from the linear groups L(2, q), q ≤ 23. Thereby we classify t-designs, t ≥ 2, admitting a transitive action of the linear groups L(2, q), q ≤ 23, up to 35 points and obtained numerous transitive designs, for 36 ≤ v ≤ 55. In many cases we proved the existence of t-designs with certain parameter sets. Among others we constructed t-designs with param...

Regular Cayley maps for finite abelian groups

A regular Cayley map for a finite group A is an orientable map whose orientation-preserving automorphism group G acts regularly on the directed edge set and has a subgroup isomorphic to A that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical ...

Regular maps with nilpotent automorphism groups

According to a folklore result, every regular map on an orientable surface with abelian automorphism group belongs to one of three infinite families of maps with one or two vertices. Here we deal with regular maps whose automorphism group is nilpotent. We show that each such map decomposes into a direct product of two maps H×K, where Aut(H) is a 2-group and K is a map with a single vertex and a...

Regular Cayley maps for nite abelian groups

Orbits of Linear Maps and Regular Languages

We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (PB-realizability problem). The decidability of the both problems is presently unknown and the first one is a straightforward generalization of the famous Skolem problem and the nonnegativity problem in t...