This paper examines abstract regular polytopes whose automorphism group is the projective special linear group PSLp4,Fqq. For q odd we show that polytopes of rank 4 exist by explicitly constructing PSLp4,Fqq as a string C-group of that rank. On the other hand, we show that no abstract regular polytope exists whose group of automorphisms is PSLp4,F2k q.

We prove the existence of two symmetric designs with parameters (256,120,56) for which the full automorphism group is isomorphic to (Z17.Z8) x (Z7.Z3).

We present a new family of locally 5–arc transitive graphs. The graphs constructed are bipartite with valency {2m + 1, 2m}. The actions of the automorphism group on the two bipartite halves are distinctly different and the corresponding amalgams are new.

This paper deals with the determination of the automorphism group of the metacyclic p-groups, P (p,m), given by the presentation P (p,m) = 〈x, y|xpm = 1, y = 1, yxy−1 = xp+1〉 (1) where p is an odd prime number and m > 1. We will show that Aut(P ) has a unique Sylow p-subgroup, Sp, and that in fact

If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation of G on Riemann-Roch space L(D).

Let (C, R) the countable dense circular ordering, and G its automorphism group. It is shown that certain properties of group elements are first order definable in G, and these results are used to reconstruct C inside G, and to demonstrate that its outer automorphism group has order 2. Similar statements hold for the completion C.

In this paper we explore the combinatorial automorphism group of the linear ordering polytope P n LO for each n > 1. We establish that this group is isomorphic to Z 2 Sym(n + 1) if n > 2 (and to Z 2 if n = 2). Doing so, we provide a simple and uniied interpretation of all the automorphisms.

Let S be a linear space with 106 points, with lines of size 6, and let G be an automorphism group of S. We prove that G cannot be point-transitive. In other words, there exists no point-transitive 2-(106, 6, 1) designs.

Every group is an outer automorphism group of a locally finite p-group. This extends an earlier result [3] about countable outer automorphism groups. It is also in sharp contrast to results concerning the existence of outer automorphisms of nilpotent groups in [6, 13, 14].

The finite flag-transitive linear spaces which have an insoluble automorphism group were given a precise description in [BDD+90], and their classification has recently been completed (see [Lie98] and [Sax02]). However, the remaining case where the automorphism group is a subgroup of one-dimensional affine transformations has not been classified and bears a variety of known examples. Here we giv...