We determine the n−automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.

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...

There exists just one regular polytope of rank larger than 3 whose full automorphism group is a projective general linear group PGL2(q), for some prime-power q. This polytope is the 4-simplex and the corresponding group is PGL2(5) ∼= S5.

On this note we prove that a holomorphic foliation of the projective plane with rich, but finite, automorphism group does not have invariant algebraic curves.

A projective plane is called a translation plane if there exists a line L such that the group of elations with axis L acts transitively on the points not on L. A translation plane whose dual plane is also a translation plane is called a semifield plane. The ternary ring corresponding to a semifield plane can be made into a non-associative algebra called a semifield, and two semifield planes are...

Two new infinite families of locally 3–arc transitive graphs are constructed which have Aut(PΩ(8, q)) as their automorphism group.

We determine, up to isomorphism, the number of abstract regular polyhedra whose automorphism group is a Suzuki simple group Sz(q) with q an odd power of 2.

The fixing number of a graph G is the minimum cardinality of a set S ⊂ V (G) such that every nonidentity automorphism of G moves at least one member of S, i.e., the automorphism group of the graph obtained from G by fixing every node in S is trivial. We provide a formula for the fixing number of a disconnected graph in terms of the fixing numbers of its components and make some observations abo...