We show that the full automorphism group of a circulant digraph of square-free order is either the intersection of two 2-closed groups, each of which is the wreath product of 2-closed groups of smaller degree, or contains a transitive normal subgroup which is the direct product of two 2-closed groups of smaller degree. The work in this paper makes contributions to the solutions of two problems ...

There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. The use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in pract...

We investigate the extent to which Slaman and Woodin’s framework for the analysis of the automorphism group of the structure of the Turing degrees can be transferred to analyze the automorphism group of the structure of the enumeration degrees.

We show that certain finite groups do not arise as the automorphism group of the square of a finite algebraic structure, nor as the automorphism group of a finite, 2-generated, free, algebraic structure.

Let R be a commutative ring and S a multiplicatively closed subset of R having no zero divisors. The pair (.R, S) is said to be stable if the ring of fractions of R, S R, defined by S is a ring for which all finitely generated projective modules are free. For a stable pair (R, S) assume 2 is a unit in R and V is a free R-module of dimension > 3. This paper examines the action of a group automor...

We prove the existence of an automorphism-invariant coupling for the wired and the free uniform spanning forests on connected graphs with residually amenable automorphism groups. MSC: 60D05, 05C05, 60B99, 20F32.

The automorphism groups for the groups of orders 8p and 8p are given. The calculations were done using the programming language CAYLEY. Explicit presentations for both the groups of these orders and their automorphism groups are given.

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 ...

In this paper we give full classification of all binary [52, 26, 10] self-dual codes with an automorphism of order 5. This completes the classification of all such codes with an automorphism of odd prim order p > 3. There are exactly 18777 such codes having an automorphism of type 5 − (10, 2). One of the constructed codes have weight enumerator W52,2 for β = 10 thus completely determines the we...

By using a lattice characterization of continuous projections defined on a topological vector space E arising from a dual pair, we determine the automorphism group of their orthomodular poset Proj(E) by means of automorphisms and anti-automorphisms of the lattice L of all closed subspaces of E. A connection between the automorphism group of the ring of all continuous linear mappings defined on ...