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 ...

Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order a...

We prove that if p is a prime and W is the standard wreath product of two nontrivial cyclic p-groups X and Y then W is isomorphic to the full automorphism group of some group if and only if |X| = 2 and |Y | is 2 or 4.

We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order p ≥ 5 have a unique cycle structure.

We introduce conditions on a group action on a tree that are sufficient for the action to extend to the automorphism group. We apply this to two different classes of one-relator groups: certain BaumslagSolitar groups and one-relator groups with centre. In each case we derive results about the automorphism group, and deduce that there are relatively few outer automorphisms.

For each q = 2m, m ≥ 1, an infinite class of 2-(q4 + q + 1, q + 1, 1) designs admitting PSU(3, q) as an automorphism group is constructed. Such designs are shown to contain embedded Desarguesian projective planes of order q and a PSU(3, q)-invariant oval. © 2013 Elsevier B.V. All rights reserved.