In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As an application of the algorithm, all the automorphism groups of semigroup of order at most 7 and of the multiplicative semigroups of some group rings ar...

Constructing symmetric drawings of graphs is NP-hard. In this paper, we present a new method for drawing graphs symmetrically based on group theory. More formally, we define an n-geometric automorphism group as a subgroup of the automorphism group of a graph that can be displayed as symmetries of a drawing of the graph in n dimensions. Then we present an algorithm to find all 2and 3-geometric a...

We construct some codes, designs and graphs that have the first or second Janko group, J1 or J2, respectively, acting as an automorphism group. We show computationally that the full automorphism group of the design or graph in each case is J1, J2 or J̄2, the extension of J2 by its outer automorphism, and we show that for some of the codes the same is true.

We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism...

This paper deals with the relation between the automorphism groups of some paving matroids and Z3, where Z3 is the additive group of modulo 3 over Z. It concludes that for paving matroids under most cases, Z3 is not isomorphic to the automorphism groups of these paving matroids. Even in the exceptional cases, we reasonably conjecture that Z3 is not isomorphic to the automorphism groups of the c...

We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a ...

This paper studies the rigidity properties of abstract commensurator outer automorphism group a universal Coxeter rank $n$, which is free product $W\_n$ $n$ copies $\mathbb{Z}/2\mathbb{Z}$. We prove that for $n\geq 5$ natural map $\mathrm{Out}(W\_n) \to \mathrm{Comm}(\mathrm{Out}(W\_n))$ an isomorphism and every between finite index subgroups $\mathrm{Out}(W\_n)$ given by a\~conjugation element...