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...

We look at AG codes associated to P, re-examining the problem of determining their automorphism groups (originally investigated by Dür in 1987 using combinatorial techniques) using recent methods from algebraic geometry. We classify those finite groups that can arise as the automorphism group of an AG code and give an explicit description of how these groups appear. We give examples of generali...

Applying a classical theorem of Smith, we show that the poset property of being Gorenstein∗ over Z2 is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. ...

In [M2], the author has defined an automorphism τ of a vertex operator algebra (VOA) of order 2 using a sub VOA isomorphic to Ising model L(12 , 0). We here define an automorphism of VOA of order 3 by using a sub VOA isomorphic to a direct sum of 3-state Potts models L(45 , 0) and an its module L( 4 5 , 3). If V is the moonshine VOA V ♮, the defined automorphism is a 3A element of the monster s...